Live_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Annotations added later for people who weren't there.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "10"
      ],
      "text/latex": [
       "10"
      ],
      "text/markdown": [
       "10"
      ],
      "text/plain": [
       "[1] 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "5+5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "9"
      ],
      "text/latex": [
       "9"
      ],
      "text/markdown": [
       "9"
      ],
      "text/plain": [
       "[1] 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "4+5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable assignment (3 identical ways)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a <- 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "5 -> a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function definition with default argument"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fn <- function(x, y = 2) {\n",
    "    x^y\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "9"
      ],
      "text/latex": [
       "9"
      ],
      "text/markdown": [
       "9"
      ],
      "text/plain": [
       "[1] 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fn(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "27"
      ],
      "text/latex": [
       "27"
      ],
      "text/markdown": [
       "27"
      ],
      "text/plain": [
       "[1] 27"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fn(3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vector data type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 1\n",
       "3. 2\n",
       "4. 3\n",
       "5. 4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0 1 2 3 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c(0,1,2,3,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shorthand for sequences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 1\n",
       "3. 2\n",
       "4. 3\n",
       "5. 4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0 1 2 3 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "0:4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v <- 10:20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "10"
      ],
      "text/latex": [
       "10"
      ],
      "text/markdown": [
       "10"
      ],
      "text/plain": [
       "[1] 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/latex": [],
      "text/markdown": [],
      "text/plain": [
       "integer(0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>11</li>\n",
       "\t<li>12</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 11\n",
       "\\item 12\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 11\n",
       "2. 12\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 11 12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v[2:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logical vectors and indexing with them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. FALSE\n",
       "6. FALSE\n",
       "7. TRUE\n",
       "8. TRUE\n",
       "9. TRUE\n",
       "10. TRUE\n",
       "11. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v > 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>16</li>\n",
       "\t<li>17</li>\n",
       "\t<li>18</li>\n",
       "\t<li>19</li>\n",
       "\t<li>20</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 16\n",
       "\\item 17\n",
       "\\item 18\n",
       "\\item 19\n",
       "\\item 20\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 16\n",
       "2. 17\n",
       "3. 18\n",
       "4. 19\n",
       "5. 20\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 16 17 18 19 20"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v[v > 15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Missing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1] NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>NA</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item NA\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 1\n",
       "3. 2\n",
       "4. NA\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  0  1  2 NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c(0, 1, 2, NA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distinct from NaN or infinity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in sqrt(-1):\n",
      "“NaNs produced”"
     ]
    },
    {
     "data": {
      "text/html": [
       "NaN"
      ],
      "text/latex": [
       "NaN"
      ],
      "text/markdown": [
       "NaN"
      ],
      "text/plain": [
       "[1] NaN"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sqrt(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "Inf"
      ],
      "text/latex": [
       "Inf"
      ],
      "text/markdown": [
       "Inf"
      ],
      "text/plain": [
       "[1] Inf"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1/0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectors with named indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pt <- c(10,20,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "names(pt) <- c(\"x\", \"y\", \"z\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>x</dt>\n",
       "\t\t<dd>10</dd>\n",
       "\t<dt>y</dt>\n",
       "\t\t<dd>20</dd>\n",
       "\t<dt>z</dt>\n",
       "\t\t<dd>30</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[x] 10\n",
       "\\item[y] 20\n",
       "\\item[z] 30\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "x\n",
       ":   10y\n",
       ":   20z\n",
       ":   30\n",
       "\n"
      ],
      "text/plain": [
       " x  y  z \n",
       "10 20 30 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>x:</strong> 10"
      ],
      "text/latex": [
       "\\textbf{x:} 10"
      ],
      "text/markdown": [
       "**x:** 10"
      ],
      "text/plain": [
       " x \n",
       "10 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt[\"x\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## List type with named indices (basically a structure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "l <- list(a = 5, n = 5, x = 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l$a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l$n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataframe (broadcasting 0 in b & c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df <- data.frame(a = 1:10, b = 0, c = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>a</th><th scope=col>b</th><th scope=col>c</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 2</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 3</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 4</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 5</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 6</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 7</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 8</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td> 9</td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><td>10</td><td>0 </td><td>0 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " a & b & c\\\\\n",
       "\\hline\n",
       "\t  1 & 0  & 0 \\\\\n",
       "\t  2 & 0  & 0 \\\\\n",
       "\t  3 & 0  & 0 \\\\\n",
       "\t  4 & 0  & 0 \\\\\n",
       "\t  5 & 0  & 0 \\\\\n",
       "\t  6 & 0  & 0 \\\\\n",
       "\t  7 & 0  & 0 \\\\\n",
       "\t  8 & 0  & 0 \\\\\n",
       "\t  9 & 0  & 0 \\\\\n",
       "\t 10 & 0  & 0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "a | b | c | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "|  1 | 0  | 0  | \n",
       "|  2 | 0  | 0  | \n",
       "|  3 | 0  | 0  | \n",
       "|  4 | 0  | 0  | \n",
       "|  5 | 0  | 0  | \n",
       "|  6 | 0  | 0  | \n",
       "|  7 | 0  | 0  | \n",
       "|  8 | 0  | 0  | \n",
       "|  9 | 0  | 0  | \n",
       "| 10 | 0  | 0  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   a  b c\n",
       "1   1 0 0\n",
       "2   2 0 0\n",
       "3   3 0 0\n",
       "4   4 0 0\n",
       "5   5 0 0\n",
       "6   6 0 0\n",
       "7   7 0 0\n",
       "8   8 0 0\n",
       "9   9 0 0\n",
       "10 10 0 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Column access shorthand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>7</li>\n",
       "\t<li>8</li>\n",
       "\t<li>9</li>\n",
       "\t<li>10</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 7\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\item 10\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "5. 5\n",
       "6. 6\n",
       "7. 7\n",
       "8. 8\n",
       "9. 9\n",
       "10. 10\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  1  2  3  4  5  6  7  8  9 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df$a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df$d <- 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>a</th><th scope=col>b</th><th scope=col>c</th><th scope=col>d</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 2</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 3</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 4</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 5</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 6</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 7</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 8</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td> 9</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><td>10</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " a & b & c & d\\\\\n",
       "\\hline\n",
       "\t  1 & 0  & 0  & 6 \\\\\n",
       "\t  2 & 0  & 0  & 6 \\\\\n",
       "\t  3 & 0  & 0  & 6 \\\\\n",
       "\t  4 & 0  & 0  & 6 \\\\\n",
       "\t  5 & 0  & 0  & 6 \\\\\n",
       "\t  6 & 0  & 0  & 6 \\\\\n",
       "\t  7 & 0  & 0  & 6 \\\\\n",
       "\t  8 & 0  & 0  & 6 \\\\\n",
       "\t  9 & 0  & 0  & 6 \\\\\n",
       "\t 10 & 0  & 0  & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "a | b | c | d | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "|  1 | 0  | 0  | 6  | \n",
       "|  2 | 0  | 0  | 6  | \n",
       "|  3 | 0  | 0  | 6  | \n",
       "|  4 | 0  | 0  | 6  | \n",
       "|  5 | 0  | 0  | 6  | \n",
       "|  6 | 0  | 0  | 6  | \n",
       "|  7 | 0  | 0  | 6  | \n",
       "|  8 | 0  | 0  | 6  | \n",
       "|  9 | 0  | 0  | 6  | \n",
       "| 10 | 0  | 0  | 6  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   a  b c d\n",
       "1   1 0 0 6\n",
       "2   2 0 0 6\n",
       "3   3 0 0 6\n",
       "4   4 0 0 6\n",
       "5   5 0 0 6\n",
       "6   6 0 0 6\n",
       "7   7 0 0 6\n",
       "8   8 0 0 6\n",
       "9   9 0 0 6\n",
       "10 10 0 0 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Column selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>a</th><th scope=col>b</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>0 </td></tr>\n",
       "\t<tr><td> 2</td><td>0 </td></tr>\n",
       "\t<tr><td> 3</td><td>0 </td></tr>\n",
       "\t<tr><td> 4</td><td>0 </td></tr>\n",
       "\t<tr><td> 5</td><td>0 </td></tr>\n",
       "\t<tr><td> 6</td><td>0 </td></tr>\n",
       "\t<tr><td> 7</td><td>0 </td></tr>\n",
       "\t<tr><td> 8</td><td>0 </td></tr>\n",
       "\t<tr><td> 9</td><td>0 </td></tr>\n",
       "\t<tr><td>10</td><td>0 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " a & b\\\\\n",
       "\\hline\n",
       "\t  1 & 0 \\\\\n",
       "\t  2 & 0 \\\\\n",
       "\t  3 & 0 \\\\\n",
       "\t  4 & 0 \\\\\n",
       "\t  5 & 0 \\\\\n",
       "\t  6 & 0 \\\\\n",
       "\t  7 & 0 \\\\\n",
       "\t  8 & 0 \\\\\n",
       "\t  9 & 0 \\\\\n",
       "\t 10 & 0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "a | b | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "|  1 | 0  | \n",
       "|  2 | 0  | \n",
       "|  3 | 0  | \n",
       "|  4 | 0  | \n",
       "|  5 | 0  | \n",
       "|  6 | 0  | \n",
       "|  7 | 0  | \n",
       "|  8 | 0  | \n",
       "|  9 | 0  | \n",
       "| 10 | 0  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   a  b\n",
       "1   1 0\n",
       "2   2 0\n",
       "3   3 0\n",
       "4   4 0\n",
       "5   5 0\n",
       "6   6 0\n",
       "7   7 0\n",
       "8   8 0\n",
       "9   9 0\n",
       "10 10 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[,c(\"a\", \"b\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Row selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>a</th><th scope=col>b</th><th scope=col>c</th><th scope=col>d</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>4</th><td>4</td><td>0</td><td>0</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>5</td><td>0</td><td>0</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>6</td><td>0</td><td>0</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>7</td><td>0</td><td>0</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       "  & a & b & c & d\\\\\n",
       "\\hline\n",
       "\t4 & 4 & 0 & 0 & 6\\\\\n",
       "\t5 & 5 & 0 & 0 & 6\\\\\n",
       "\t6 & 6 & 0 & 0 & 6\\\\\n",
       "\t7 & 7 & 0 & 0 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | a | b | c | d | \n",
       "|---|---|---|---|\n",
       "| 4 | 4 | 0 | 0 | 6 | \n",
       "| 5 | 5 | 0 | 0 | 6 | \n",
       "| 6 | 6 | 0 | 0 | 6 | \n",
       "| 7 | 7 | 0 | 0 | 6 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  a b c d\n",
       "4 4 0 0 6\n",
       "5 5 0 0 6\n",
       "6 6 0 0 6\n",
       "7 7 0 0 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[4:7,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Row and column selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>c</th><th scope=col>d</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>5</th><td>0</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & c & d\\\\\n",
       "\\hline\n",
       "\t5 & 0 & 6\\\\\n",
       "\t6 & 0 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | c | d | \n",
       "|---|---|\n",
       "| 5 | 0 | 6 | \n",
       "| 6 | 0 | 6 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  c d\n",
       "5 0 6\n",
       "6 0 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[c(5,6), c(\"c\", \"d\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logical vector, used to filter rows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. FALSE\n",
       "6. TRUE\n",
       "7. TRUE\n",
       "8. TRUE\n",
       "9. TRUE\n",
       "10. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c <- df$a > 5\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>a</th><th scope=col>b</th><th scope=col>c</th><th scope=col>d</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>0 </td><td>0 </td><td>6 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       "  & a & b & c & d\\\\\n",
       "\\hline\n",
       "\t6 &  6 & 0  & 0  & 6 \\\\\n",
       "\t7 &  7 & 0  & 0  & 6 \\\\\n",
       "\t8 &  8 & 0  & 0  & 6 \\\\\n",
       "\t9 &  9 & 0  & 0  & 6 \\\\\n",
       "\t10 & 10 & 0  & 0  & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | a | b | c | d | \n",
       "|---|---|---|---|---|\n",
       "| 6 |  6 | 0  | 0  | 6  | \n",
       "| 7 |  7 | 0  | 0  | 6  | \n",
       "| 8 |  8 | 0  | 0  | 6  | \n",
       "| 9 |  9 | 0  | 0  | 6  | \n",
       "| 10 | 10 | 0  | 0  | 6  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   a  b c d\n",
       "6   6 0 0 6\n",
       "7   7 0 0 6\n",
       "8   8 0 0 6\n",
       "9   9 0 0 6\n",
       "10 10 0 0 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[c,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Built-in dataset & dplyr examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This won't show results in the notebook,\n",
    "# but rather in a separate pop-up; this and\n",
    "# help() will invoke R's documentation\n",
    "? mtcars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘dplyr’\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(dplyr)\n",
    "mtcars2 <- tibble::rownames_to_column(mtcars) %>% rename(car= rowname)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Mazda RX4</th><td>21.0 </td><td>6    </td><td>160.0</td><td>110  </td><td>3.90 </td><td>2.620</td><td>16.46</td><td>0    </td><td>1    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Mazda RX4 Wag</th><td>21.0 </td><td>6    </td><td>160.0</td><td>110  </td><td>3.90 </td><td>2.875</td><td>17.02</td><td>0    </td><td>1    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Datsun 710</th><td>22.8 </td><td>4    </td><td>108.0</td><td> 93  </td><td>3.85 </td><td>2.320</td><td>18.61</td><td>1    </td><td>1    </td><td>4    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Hornet 4 Drive</th><td>21.4 </td><td>6    </td><td>258.0</td><td>110  </td><td>3.08 </td><td>3.215</td><td>19.44</td><td>1    </td><td>0    </td><td>3    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Hornet Sportabout</th><td>18.7 </td><td>8    </td><td>360.0</td><td>175  </td><td>3.15 </td><td>3.440</td><td>17.02</td><td>0    </td><td>0    </td><td>3    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Valiant</th><td>18.1 </td><td>6    </td><td>225.0</td><td>105  </td><td>2.76 </td><td>3.460</td><td>20.22</td><td>1    </td><td>0    </td><td>3    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Duster 360</th><td>14.3 </td><td>8    </td><td>360.0</td><td>245  </td><td>3.21 </td><td>3.570</td><td>15.84</td><td>0    </td><td>0    </td><td>3    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Merc 240D</th><td>24.4 </td><td>4    </td><td>146.7</td><td> 62  </td><td>3.69 </td><td>3.190</td><td>20.00</td><td>1    </td><td>0    </td><td>4    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Merc 230</th><td>22.8 </td><td>4    </td><td>140.8</td><td> 95  </td><td>3.92 </td><td>3.150</td><td>22.90</td><td>1    </td><td>0    </td><td>4    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Merc 280</th><td>19.2 </td><td>6    </td><td>167.6</td><td>123  </td><td>3.92 </td><td>3.440</td><td>18.30</td><td>1    </td><td>0    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Merc 280C</th><td>17.8 </td><td>6    </td><td>167.6</td><td>123  </td><td>3.92 </td><td>3.440</td><td>18.90</td><td>1    </td><td>0    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Merc 450SE</th><td>16.4 </td><td>8    </td><td>275.8</td><td>180  </td><td>3.07 </td><td>4.070</td><td>17.40</td><td>0    </td><td>0    </td><td>3    </td><td>3    </td></tr>\n",
       "\t<tr><th scope=row>Merc 450SL</th><td>17.3 </td><td>8    </td><td>275.8</td><td>180  </td><td>3.07 </td><td>3.730</td><td>17.60</td><td>0    </td><td>0    </td><td>3    </td><td>3    </td></tr>\n",
       "\t<tr><th scope=row>Merc 450SLC</th><td>15.2 </td><td>8    </td><td>275.8</td><td>180  </td><td>3.07 </td><td>3.780</td><td>18.00</td><td>0    </td><td>0    </td><td>3    </td><td>3    </td></tr>\n",
       "\t<tr><th scope=row>Cadillac Fleetwood</th><td>10.4 </td><td>8    </td><td>472.0</td><td>205  </td><td>2.93 </td><td>5.250</td><td>17.98</td><td>0    </td><td>0    </td><td>3    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Lincoln Continental</th><td>10.4 </td><td>8    </td><td>460.0</td><td>215  </td><td>3.00 </td><td>5.424</td><td>17.82</td><td>0    </td><td>0    </td><td>3    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Chrysler Imperial</th><td>14.7 </td><td>8    </td><td>440.0</td><td>230  </td><td>3.23 </td><td>5.345</td><td>17.42</td><td>0    </td><td>0    </td><td>3    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Fiat 128</th><td>32.4 </td><td>4    </td><td> 78.7</td><td> 66  </td><td>4.08 </td><td>2.200</td><td>19.47</td><td>1    </td><td>1    </td><td>4    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Honda Civic</th><td>30.4 </td><td>4    </td><td> 75.7</td><td> 52  </td><td>4.93 </td><td>1.615</td><td>18.52</td><td>1    </td><td>1    </td><td>4    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Toyota Corolla</th><td>33.9 </td><td>4    </td><td> 71.1</td><td> 65  </td><td>4.22 </td><td>1.835</td><td>19.90</td><td>1    </td><td>1    </td><td>4    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Toyota Corona</th><td>21.5 </td><td>4    </td><td>120.1</td><td> 97  </td><td>3.70 </td><td>2.465</td><td>20.01</td><td>1    </td><td>0    </td><td>3    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Dodge Challenger</th><td>15.5 </td><td>8    </td><td>318.0</td><td>150  </td><td>2.76 </td><td>3.520</td><td>16.87</td><td>0    </td><td>0    </td><td>3    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>AMC Javelin</th><td>15.2 </td><td>8    </td><td>304.0</td><td>150  </td><td>3.15 </td><td>3.435</td><td>17.30</td><td>0    </td><td>0    </td><td>3    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Camaro Z28</th><td>13.3 </td><td>8    </td><td>350.0</td><td>245  </td><td>3.73 </td><td>3.840</td><td>15.41</td><td>0    </td><td>0    </td><td>3    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Pontiac Firebird</th><td>19.2 </td><td>8    </td><td>400.0</td><td>175  </td><td>3.08 </td><td>3.845</td><td>17.05</td><td>0    </td><td>0    </td><td>3    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Fiat X1-9</th><td>27.3 </td><td>4    </td><td> 79.0</td><td> 66  </td><td>4.08 </td><td>1.935</td><td>18.90</td><td>1    </td><td>1    </td><td>4    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Porsche 914-2</th><td>26.0 </td><td>4    </td><td>120.3</td><td> 91  </td><td>4.43 </td><td>2.140</td><td>16.70</td><td>0    </td><td>1    </td><td>5    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Lotus Europa</th><td>30.4 </td><td>4    </td><td> 95.1</td><td>113  </td><td>3.77 </td><td>1.513</td><td>16.90</td><td>1    </td><td>1    </td><td>5    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Ford Pantera L</th><td>15.8 </td><td>8    </td><td>351.0</td><td>264  </td><td>4.22 </td><td>3.170</td><td>14.50</td><td>0    </td><td>1    </td><td>5    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Ferrari Dino</th><td>19.7 </td><td>6    </td><td>145.0</td><td>175  </td><td>3.62 </td><td>2.770</td><td>15.50</td><td>0    </td><td>1    </td><td>5    </td><td>6    </td></tr>\n",
       "\t<tr><th scope=row>Maserati Bora</th><td>15.0 </td><td>8    </td><td>301.0</td><td>335  </td><td>3.54 </td><td>3.570</td><td>14.60</td><td>0    </td><td>1    </td><td>5    </td><td>8    </td></tr>\n",
       "\t<tr><th scope=row>Volvo 142E</th><td>21.4 </td><td>4    </td><td>121.0</td><td>109  </td><td>4.11 </td><td>2.780</td><td>18.60</td><td>1    </td><td>1    </td><td>4    </td><td>2    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       "  & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n",
       "\\hline\n",
       "\tMazda RX4 & 21.0  & 6     & 160.0 & 110   & 3.90  & 2.620 & 16.46 & 0     & 1     & 4     & 4    \\\\\n",
       "\tMazda RX4 Wag & 21.0  & 6     & 160.0 & 110   & 3.90  & 2.875 & 17.02 & 0     & 1     & 4     & 4    \\\\\n",
       "\tDatsun 710 & 22.8  & 4     & 108.0 &  93   & 3.85  & 2.320 & 18.61 & 1     & 1     & 4     & 1    \\\\\n",
       "\tHornet 4 Drive & 21.4  & 6     & 258.0 & 110   & 3.08  & 3.215 & 19.44 & 1     & 0     & 3     & 1    \\\\\n",
       "\tHornet Sportabout & 18.7  & 8     & 360.0 & 175   & 3.15  & 3.440 & 17.02 & 0     & 0     & 3     & 2    \\\\\n",
       "\tValiant & 18.1  & 6     & 225.0 & 105   & 2.76  & 3.460 & 20.22 & 1     & 0     & 3     & 1    \\\\\n",
       "\tDuster 360 & 14.3  & 8     & 360.0 & 245   & 3.21  & 3.570 & 15.84 & 0     & 0     & 3     & 4    \\\\\n",
       "\tMerc 240D & 24.4  & 4     & 146.7 &  62   & 3.69  & 3.190 & 20.00 & 1     & 0     & 4     & 2    \\\\\n",
       "\tMerc 230 & 22.8  & 4     & 140.8 &  95   & 3.92  & 3.150 & 22.90 & 1     & 0     & 4     & 2    \\\\\n",
       "\tMerc 280 & 19.2  & 6     & 167.6 & 123   & 3.92  & 3.440 & 18.30 & 1     & 0     & 4     & 4    \\\\\n",
       "\tMerc 280C & 17.8  & 6     & 167.6 & 123   & 3.92  & 3.440 & 18.90 & 1     & 0     & 4     & 4    \\\\\n",
       "\tMerc 450SE & 16.4  & 8     & 275.8 & 180   & 3.07  & 4.070 & 17.40 & 0     & 0     & 3     & 3    \\\\\n",
       "\tMerc 450SL & 17.3  & 8     & 275.8 & 180   & 3.07  & 3.730 & 17.60 & 0     & 0     & 3     & 3    \\\\\n",
       "\tMerc 450SLC & 15.2  & 8     & 275.8 & 180   & 3.07  & 3.780 & 18.00 & 0     & 0     & 3     & 3    \\\\\n",
       "\tCadillac Fleetwood & 10.4  & 8     & 472.0 & 205   & 2.93  & 5.250 & 17.98 & 0     & 0     & 3     & 4    \\\\\n",
       "\tLincoln Continental & 10.4  & 8     & 460.0 & 215   & 3.00  & 5.424 & 17.82 & 0     & 0     & 3     & 4    \\\\\n",
       "\tChrysler Imperial & 14.7  & 8     & 440.0 & 230   & 3.23  & 5.345 & 17.42 & 0     & 0     & 3     & 4    \\\\\n",
       "\tFiat 128 & 32.4  & 4     &  78.7 &  66   & 4.08  & 2.200 & 19.47 & 1     & 1     & 4     & 1    \\\\\n",
       "\tHonda Civic & 30.4  & 4     &  75.7 &  52   & 4.93  & 1.615 & 18.52 & 1     & 1     & 4     & 2    \\\\\n",
       "\tToyota Corolla & 33.9  & 4     &  71.1 &  65   & 4.22  & 1.835 & 19.90 & 1     & 1     & 4     & 1    \\\\\n",
       "\tToyota Corona & 21.5  & 4     & 120.1 &  97   & 3.70  & 2.465 & 20.01 & 1     & 0     & 3     & 1    \\\\\n",
       "\tDodge Challenger & 15.5  & 8     & 318.0 & 150   & 2.76  & 3.520 & 16.87 & 0     & 0     & 3     & 2    \\\\\n",
       "\tAMC Javelin & 15.2  & 8     & 304.0 & 150   & 3.15  & 3.435 & 17.30 & 0     & 0     & 3     & 2    \\\\\n",
       "\tCamaro Z28 & 13.3  & 8     & 350.0 & 245   & 3.73  & 3.840 & 15.41 & 0     & 0     & 3     & 4    \\\\\n",
       "\tPontiac Firebird & 19.2  & 8     & 400.0 & 175   & 3.08  & 3.845 & 17.05 & 0     & 0     & 3     & 2    \\\\\n",
       "\tFiat X1-9 & 27.3  & 4     &  79.0 &  66   & 4.08  & 1.935 & 18.90 & 1     & 1     & 4     & 1    \\\\\n",
       "\tPorsche 914-2 & 26.0  & 4     & 120.3 &  91   & 4.43  & 2.140 & 16.70 & 0     & 1     & 5     & 2    \\\\\n",
       "\tLotus Europa & 30.4  & 4     &  95.1 & 113   & 3.77  & 1.513 & 16.90 & 1     & 1     & 5     & 2    \\\\\n",
       "\tFord Pantera L & 15.8  & 8     & 351.0 & 264   & 4.22  & 3.170 & 14.50 & 0     & 1     & 5     & 4    \\\\\n",
       "\tFerrari Dino & 19.7  & 6     & 145.0 & 175   & 3.62  & 2.770 & 15.50 & 0     & 1     & 5     & 6    \\\\\n",
       "\tMaserati Bora & 15.0  & 8     & 301.0 & 335   & 3.54  & 3.570 & 14.60 & 0     & 1     & 5     & 8    \\\\\n",
       "\tVolvo 142E & 21.4  & 4     & 121.0 & 109   & 4.11  & 2.780 & 18.60 & 1     & 1     & 4     & 2    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| Mazda RX4 | 21.0  | 6     | 160.0 | 110   | 3.90  | 2.620 | 16.46 | 0     | 1     | 4     | 4     | \n",
       "| Mazda RX4 Wag | 21.0  | 6     | 160.0 | 110   | 3.90  | 2.875 | 17.02 | 0     | 1     | 4     | 4     | \n",
       "| Datsun 710 | 22.8  | 4     | 108.0 |  93   | 3.85  | 2.320 | 18.61 | 1     | 1     | 4     | 1     | \n",
       "| Hornet 4 Drive | 21.4  | 6     | 258.0 | 110   | 3.08  | 3.215 | 19.44 | 1     | 0     | 3     | 1     | \n",
       "| Hornet Sportabout | 18.7  | 8     | 360.0 | 175   | 3.15  | 3.440 | 17.02 | 0     | 0     | 3     | 2     | \n",
       "| Valiant | 18.1  | 6     | 225.0 | 105   | 2.76  | 3.460 | 20.22 | 1     | 0     | 3     | 1     | \n",
       "| Duster 360 | 14.3  | 8     | 360.0 | 245   | 3.21  | 3.570 | 15.84 | 0     | 0     | 3     | 4     | \n",
       "| Merc 240D | 24.4  | 4     | 146.7 |  62   | 3.69  | 3.190 | 20.00 | 1     | 0     | 4     | 2     | \n",
       "| Merc 230 | 22.8  | 4     | 140.8 |  95   | 3.92  | 3.150 | 22.90 | 1     | 0     | 4     | 2     | \n",
       "| Merc 280 | 19.2  | 6     | 167.6 | 123   | 3.92  | 3.440 | 18.30 | 1     | 0     | 4     | 4     | \n",
       "| Merc 280C | 17.8  | 6     | 167.6 | 123   | 3.92  | 3.440 | 18.90 | 1     | 0     | 4     | 4     | \n",
       "| Merc 450SE | 16.4  | 8     | 275.8 | 180   | 3.07  | 4.070 | 17.40 | 0     | 0     | 3     | 3     | \n",
       "| Merc 450SL | 17.3  | 8     | 275.8 | 180   | 3.07  | 3.730 | 17.60 | 0     | 0     | 3     | 3     | \n",
       "| Merc 450SLC | 15.2  | 8     | 275.8 | 180   | 3.07  | 3.780 | 18.00 | 0     | 0     | 3     | 3     | \n",
       "| Cadillac Fleetwood | 10.4  | 8     | 472.0 | 205   | 2.93  | 5.250 | 17.98 | 0     | 0     | 3     | 4     | \n",
       "| Lincoln Continental | 10.4  | 8     | 460.0 | 215   | 3.00  | 5.424 | 17.82 | 0     | 0     | 3     | 4     | \n",
       "| Chrysler Imperial | 14.7  | 8     | 440.0 | 230   | 3.23  | 5.345 | 17.42 | 0     | 0     | 3     | 4     | \n",
       "| Fiat 128 | 32.4  | 4     |  78.7 |  66   | 4.08  | 2.200 | 19.47 | 1     | 1     | 4     | 1     | \n",
       "| Honda Civic | 30.4  | 4     |  75.7 |  52   | 4.93  | 1.615 | 18.52 | 1     | 1     | 4     | 2     | \n",
       "| Toyota Corolla | 33.9  | 4     |  71.1 |  65   | 4.22  | 1.835 | 19.90 | 1     | 1     | 4     | 1     | \n",
       "| Toyota Corona | 21.5  | 4     | 120.1 |  97   | 3.70  | 2.465 | 20.01 | 1     | 0     | 3     | 1     | \n",
       "| Dodge Challenger | 15.5  | 8     | 318.0 | 150   | 2.76  | 3.520 | 16.87 | 0     | 0     | 3     | 2     | \n",
       "| AMC Javelin | 15.2  | 8     | 304.0 | 150   | 3.15  | 3.435 | 17.30 | 0     | 0     | 3     | 2     | \n",
       "| Camaro Z28 | 13.3  | 8     | 350.0 | 245   | 3.73  | 3.840 | 15.41 | 0     | 0     | 3     | 4     | \n",
       "| Pontiac Firebird | 19.2  | 8     | 400.0 | 175   | 3.08  | 3.845 | 17.05 | 0     | 0     | 3     | 2     | \n",
       "| Fiat X1-9 | 27.3  | 4     |  79.0 |  66   | 4.08  | 1.935 | 18.90 | 1     | 1     | 4     | 1     | \n",
       "| Porsche 914-2 | 26.0  | 4     | 120.3 |  91   | 4.43  | 2.140 | 16.70 | 0     | 1     | 5     | 2     | \n",
       "| Lotus Europa | 30.4  | 4     |  95.1 | 113   | 3.77  | 1.513 | 16.90 | 1     | 1     | 5     | 2     | \n",
       "| Ford Pantera L | 15.8  | 8     | 351.0 | 264   | 4.22  | 3.170 | 14.50 | 0     | 1     | 5     | 4     | \n",
       "| Ferrari Dino | 19.7  | 6     | 145.0 | 175   | 3.62  | 2.770 | 15.50 | 0     | 1     | 5     | 6     | \n",
       "| Maserati Bora | 15.0  | 8     | 301.0 | 335   | 3.54  | 3.570 | 14.60 | 0     | 1     | 5     | 8     | \n",
       "| Volvo 142E | 21.4  | 4     | 121.0 | 109   | 4.11  | 2.780 | 18.60 | 1     | 1     | 4     | 2     | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                    mpg  cyl disp  hp  drat wt    qsec  vs am gear carb\n",
       "Mazda RX4           21.0 6   160.0 110 3.90 2.620 16.46 0  1  4    4   \n",
       "Mazda RX4 Wag       21.0 6   160.0 110 3.90 2.875 17.02 0  1  4    4   \n",
       "Datsun 710          22.8 4   108.0  93 3.85 2.320 18.61 1  1  4    1   \n",
       "Hornet 4 Drive      21.4 6   258.0 110 3.08 3.215 19.44 1  0  3    1   \n",
       "Hornet Sportabout   18.7 8   360.0 175 3.15 3.440 17.02 0  0  3    2   \n",
       "Valiant             18.1 6   225.0 105 2.76 3.460 20.22 1  0  3    1   \n",
       "Duster 360          14.3 8   360.0 245 3.21 3.570 15.84 0  0  3    4   \n",
       "Merc 240D           24.4 4   146.7  62 3.69 3.190 20.00 1  0  4    2   \n",
       "Merc 230            22.8 4   140.8  95 3.92 3.150 22.90 1  0  4    2   \n",
       "Merc 280            19.2 6   167.6 123 3.92 3.440 18.30 1  0  4    4   \n",
       "Merc 280C           17.8 6   167.6 123 3.92 3.440 18.90 1  0  4    4   \n",
       "Merc 450SE          16.4 8   275.8 180 3.07 4.070 17.40 0  0  3    3   \n",
       "Merc 450SL          17.3 8   275.8 180 3.07 3.730 17.60 0  0  3    3   \n",
       "Merc 450SLC         15.2 8   275.8 180 3.07 3.780 18.00 0  0  3    3   \n",
       "Cadillac Fleetwood  10.4 8   472.0 205 2.93 5.250 17.98 0  0  3    4   \n",
       "Lincoln Continental 10.4 8   460.0 215 3.00 5.424 17.82 0  0  3    4   \n",
       "Chrysler Imperial   14.7 8   440.0 230 3.23 5.345 17.42 0  0  3    4   \n",
       "Fiat 128            32.4 4    78.7  66 4.08 2.200 19.47 1  1  4    1   \n",
       "Honda Civic         30.4 4    75.7  52 4.93 1.615 18.52 1  1  4    2   \n",
       "Toyota Corolla      33.9 4    71.1  65 4.22 1.835 19.90 1  1  4    1   \n",
       "Toyota Corona       21.5 4   120.1  97 3.70 2.465 20.01 1  0  3    1   \n",
       "Dodge Challenger    15.5 8   318.0 150 2.76 3.520 16.87 0  0  3    2   \n",
       "AMC Javelin         15.2 8   304.0 150 3.15 3.435 17.30 0  0  3    2   \n",
       "Camaro Z28          13.3 8   350.0 245 3.73 3.840 15.41 0  0  3    4   \n",
       "Pontiac Firebird    19.2 8   400.0 175 3.08 3.845 17.05 0  0  3    2   \n",
       "Fiat X1-9           27.3 4    79.0  66 4.08 1.935 18.90 1  1  4    1   \n",
       "Porsche 914-2       26.0 4   120.3  91 4.43 2.140 16.70 0  1  5    2   \n",
       "Lotus Europa        30.4 4    95.1 113 3.77 1.513 16.90 1  1  5    2   \n",
       "Ford Pantera L      15.8 8   351.0 264 4.22 3.170 14.50 0  1  5    4   \n",
       "Ferrari Dino        19.7 6   145.0 175 3.62 2.770 15.50 0  1  5    6   \n",
       "Maserati Bora       15.0 8   301.0 335 3.54 3.570 14.60 0  1  5    8   \n",
       "Volvo 142E          21.4 4   121.0 109 4.11 2.780 18.60 1  1  4    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mtcars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>car</th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Mazda RX4          </td><td>21.0               </td><td>6                  </td><td>160.0              </td><td>110                </td><td>3.90               </td><td>2.620              </td><td>16.46              </td><td>0                  </td><td>1                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Mazda RX4 Wag      </td><td>21.0               </td><td>6                  </td><td>160.0              </td><td>110                </td><td>3.90               </td><td>2.875              </td><td>17.02              </td><td>0                  </td><td>1                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Datsun 710         </td><td>22.8               </td><td>4                  </td><td>108.0              </td><td> 93                </td><td>3.85               </td><td>2.320              </td><td>18.61              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Hornet 4 Drive     </td><td>21.4               </td><td>6                  </td><td>258.0              </td><td>110                </td><td>3.08               </td><td>3.215              </td><td>19.44              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Hornet Sportabout  </td><td>18.7               </td><td>8                  </td><td>360.0              </td><td>175                </td><td>3.15               </td><td>3.440              </td><td>17.02              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Valiant            </td><td>18.1               </td><td>6                  </td><td>225.0              </td><td>105                </td><td>2.76               </td><td>3.460              </td><td>20.22              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Duster 360         </td><td>14.3               </td><td>8                  </td><td>360.0              </td><td>245                </td><td>3.21               </td><td>3.570              </td><td>15.84              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Merc 240D          </td><td>24.4               </td><td>4                  </td><td>146.7              </td><td> 62                </td><td>3.69               </td><td>3.190              </td><td>20.00              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Merc 230           </td><td>22.8               </td><td>4                  </td><td>140.8              </td><td> 95                </td><td>3.92               </td><td>3.150              </td><td>22.90              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Merc 280           </td><td>19.2               </td><td>6                  </td><td>167.6              </td><td>123                </td><td>3.92               </td><td>3.440              </td><td>18.30              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Merc 280C          </td><td>17.8               </td><td>6                  </td><td>167.6              </td><td>123                </td><td>3.92               </td><td>3.440              </td><td>18.90              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Merc 450SE         </td><td>16.4               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>4.070              </td><td>17.40              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>Merc 450SL         </td><td>17.3               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>3.730              </td><td>17.60              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>Merc 450SLC        </td><td>15.2               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>3.780              </td><td>18.00              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>Cadillac Fleetwood </td><td>10.4               </td><td>8                  </td><td>472.0              </td><td>205                </td><td>2.93               </td><td>5.250              </td><td>17.98              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Lincoln Continental</td><td>10.4               </td><td>8                  </td><td>460.0              </td><td>215                </td><td>3.00               </td><td>5.424              </td><td>17.82              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Chrysler Imperial  </td><td>14.7               </td><td>8                  </td><td>440.0              </td><td>230                </td><td>3.23               </td><td>5.345              </td><td>17.42              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Fiat 128           </td><td>32.4               </td><td>4                  </td><td> 78.7              </td><td> 66                </td><td>4.08               </td><td>2.200              </td><td>19.47              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Honda Civic        </td><td>30.4               </td><td>4                  </td><td> 75.7              </td><td> 52                </td><td>4.93               </td><td>1.615              </td><td>18.52              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Toyota Corolla     </td><td>33.9               </td><td>4                  </td><td> 71.1              </td><td> 65                </td><td>4.22               </td><td>1.835              </td><td>19.90              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Toyota Corona      </td><td>21.5               </td><td>4                  </td><td>120.1              </td><td> 97                </td><td>3.70               </td><td>2.465              </td><td>20.01              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Dodge Challenger   </td><td>15.5               </td><td>8                  </td><td>318.0              </td><td>150                </td><td>2.76               </td><td>3.520              </td><td>16.87              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>AMC Javelin        </td><td>15.2               </td><td>8                  </td><td>304.0              </td><td>150                </td><td>3.15               </td><td>3.435              </td><td>17.30              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Camaro Z28         </td><td>13.3               </td><td>8                  </td><td>350.0              </td><td>245                </td><td>3.73               </td><td>3.840              </td><td>15.41              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Pontiac Firebird   </td><td>19.2               </td><td>8                  </td><td>400.0              </td><td>175                </td><td>3.08               </td><td>3.845              </td><td>17.05              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Fiat X1-9          </td><td>27.3               </td><td>4                  </td><td> 79.0              </td><td> 66                </td><td>4.08               </td><td>1.935              </td><td>18.90              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Porsche 914-2      </td><td>26.0               </td><td>4                  </td><td>120.3              </td><td> 91                </td><td>4.43               </td><td>2.140              </td><td>16.70              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Lotus Europa       </td><td>30.4               </td><td>4                  </td><td> 95.1              </td><td>113                </td><td>3.77               </td><td>1.513              </td><td>16.90              </td><td>1                  </td><td>1                  </td><td>5                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Ford Pantera L     </td><td>15.8               </td><td>8                  </td><td>351.0              </td><td>264                </td><td>4.22               </td><td>3.170              </td><td>14.50              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Ferrari Dino       </td><td>19.7               </td><td>6                  </td><td>145.0              </td><td>175                </td><td>3.62               </td><td>2.770              </td><td>15.50              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>6                  </td></tr>\n",
       "\t<tr><td>Maserati Bora      </td><td>15.0               </td><td>8                  </td><td>301.0              </td><td>335                </td><td>3.54               </td><td>3.570              </td><td>14.60              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>8                  </td></tr>\n",
       "\t<tr><td>Volvo 142E         </td><td>21.4               </td><td>4                  </td><td>121.0              </td><td>109                </td><td>4.11               </td><td>2.780              </td><td>18.60              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllll}\n",
       " car & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n",
       "\\hline\n",
       "\t Mazda RX4           & 21.0                & 6                   & 160.0               & 110                 & 3.90                & 2.620               & 16.46               & 0                   & 1                   & 4                   & 4                  \\\\\n",
       "\t Mazda RX4 Wag       & 21.0                & 6                   & 160.0               & 110                 & 3.90                & 2.875               & 17.02               & 0                   & 1                   & 4                   & 4                  \\\\\n",
       "\t Datsun 710          & 22.8                & 4                   & 108.0               &  93                 & 3.85                & 2.320               & 18.61               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Hornet 4 Drive      & 21.4                & 6                   & 258.0               & 110                 & 3.08                & 3.215               & 19.44               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Hornet Sportabout   & 18.7                & 8                   & 360.0               & 175                 & 3.15                & 3.440               & 17.02               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Valiant             & 18.1                & 6                   & 225.0               & 105                 & 2.76                & 3.460               & 20.22               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Duster 360          & 14.3                & 8                   & 360.0               & 245                 & 3.21                & 3.570               & 15.84               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Merc 240D           & 24.4                & 4                   & 146.7               &  62                 & 3.69                & 3.190               & 20.00               & 1                   & 0                   & 4                   & 2                  \\\\\n",
       "\t Merc 230            & 22.8                & 4                   & 140.8               &  95                 & 3.92                & 3.150               & 22.90               & 1                   & 0                   & 4                   & 2                  \\\\\n",
       "\t Merc 280            & 19.2                & 6                   & 167.6               & 123                 & 3.92                & 3.440               & 18.30               & 1                   & 0                   & 4                   & 4                  \\\\\n",
       "\t Merc 280C           & 17.8                & 6                   & 167.6               & 123                 & 3.92                & 3.440               & 18.90               & 1                   & 0                   & 4                   & 4                  \\\\\n",
       "\t Merc 450SE          & 16.4                & 8                   & 275.8               & 180                 & 3.07                & 4.070               & 17.40               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t Merc 450SL          & 17.3                & 8                   & 275.8               & 180                 & 3.07                & 3.730               & 17.60               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t Merc 450SLC         & 15.2                & 8                   & 275.8               & 180                 & 3.07                & 3.780               & 18.00               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t Cadillac Fleetwood  & 10.4                & 8                   & 472.0               & 205                 & 2.93                & 5.250               & 17.98               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Lincoln Continental & 10.4                & 8                   & 460.0               & 215                 & 3.00                & 5.424               & 17.82               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Chrysler Imperial   & 14.7                & 8                   & 440.0               & 230                 & 3.23                & 5.345               & 17.42               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Fiat 128            & 32.4                & 4                   &  78.7               &  66                 & 4.08                & 2.200               & 19.47               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Honda Civic         & 30.4                & 4                   &  75.7               &  52                 & 4.93                & 1.615               & 18.52               & 1                   & 1                   & 4                   & 2                  \\\\\n",
       "\t Toyota Corolla      & 33.9                & 4                   &  71.1               &  65                 & 4.22                & 1.835               & 19.90               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Toyota Corona       & 21.5                & 4                   & 120.1               &  97                 & 3.70                & 2.465               & 20.01               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Dodge Challenger    & 15.5                & 8                   & 318.0               & 150                 & 2.76                & 3.520               & 16.87               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t AMC Javelin         & 15.2                & 8                   & 304.0               & 150                 & 3.15                & 3.435               & 17.30               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Camaro Z28          & 13.3                & 8                   & 350.0               & 245                 & 3.73                & 3.840               & 15.41               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Pontiac Firebird    & 19.2                & 8                   & 400.0               & 175                 & 3.08                & 3.845               & 17.05               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Fiat X1-9           & 27.3                & 4                   &  79.0               &  66                 & 4.08                & 1.935               & 18.90               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Porsche 914-2       & 26.0                & 4                   & 120.3               &  91                 & 4.43                & 2.140               & 16.70               & 0                   & 1                   & 5                   & 2                  \\\\\n",
       "\t Lotus Europa        & 30.4                & 4                   &  95.1               & 113                 & 3.77                & 1.513               & 16.90               & 1                   & 1                   & 5                   & 2                  \\\\\n",
       "\t Ford Pantera L      & 15.8                & 8                   & 351.0               & 264                 & 4.22                & 3.170               & 14.50               & 0                   & 1                   & 5                   & 4                  \\\\\n",
       "\t Ferrari Dino        & 19.7                & 6                   & 145.0               & 175                 & 3.62                & 2.770               & 15.50               & 0                   & 1                   & 5                   & 6                  \\\\\n",
       "\t Maserati Bora       & 15.0                & 8                   & 301.0               & 335                 & 3.54                & 3.570               & 14.60               & 0                   & 1                   & 5                   & 8                  \\\\\n",
       "\t Volvo 142E          & 21.4                & 4                   & 121.0               & 109                 & 4.11                & 2.780               & 18.60               & 1                   & 1                   & 4                   & 2                  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "car | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| Mazda RX4           | 21.0                | 6                   | 160.0               | 110                 | 3.90                | 2.620               | 16.46               | 0                   | 1                   | 4                   | 4                   | \n",
       "| Mazda RX4 Wag       | 21.0                | 6                   | 160.0               | 110                 | 3.90                | 2.875               | 17.02               | 0                   | 1                   | 4                   | 4                   | \n",
       "| Datsun 710          | 22.8                | 4                   | 108.0               |  93                 | 3.85                | 2.320               | 18.61               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Hornet 4 Drive      | 21.4                | 6                   | 258.0               | 110                 | 3.08                | 3.215               | 19.44               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Hornet Sportabout   | 18.7                | 8                   | 360.0               | 175                 | 3.15                | 3.440               | 17.02               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Valiant             | 18.1                | 6                   | 225.0               | 105                 | 2.76                | 3.460               | 20.22               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Duster 360          | 14.3                | 8                   | 360.0               | 245                 | 3.21                | 3.570               | 15.84               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Merc 240D           | 24.4                | 4                   | 146.7               |  62                 | 3.69                | 3.190               | 20.00               | 1                   | 0                   | 4                   | 2                   | \n",
       "| Merc 230            | 22.8                | 4                   | 140.8               |  95                 | 3.92                | 3.150               | 22.90               | 1                   | 0                   | 4                   | 2                   | \n",
       "| Merc 280            | 19.2                | 6                   | 167.6               | 123                 | 3.92                | 3.440               | 18.30               | 1                   | 0                   | 4                   | 4                   | \n",
       "| Merc 280C           | 17.8                | 6                   | 167.6               | 123                 | 3.92                | 3.440               | 18.90               | 1                   | 0                   | 4                   | 4                   | \n",
       "| Merc 450SE          | 16.4                | 8                   | 275.8               | 180                 | 3.07                | 4.070               | 17.40               | 0                   | 0                   | 3                   | 3                   | \n",
       "| Merc 450SL          | 17.3                | 8                   | 275.8               | 180                 | 3.07                | 3.730               | 17.60               | 0                   | 0                   | 3                   | 3                   | \n",
       "| Merc 450SLC         | 15.2                | 8                   | 275.8               | 180                 | 3.07                | 3.780               | 18.00               | 0                   | 0                   | 3                   | 3                   | \n",
       "| Cadillac Fleetwood  | 10.4                | 8                   | 472.0               | 205                 | 2.93                | 5.250               | 17.98               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Lincoln Continental | 10.4                | 8                   | 460.0               | 215                 | 3.00                | 5.424               | 17.82               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Chrysler Imperial   | 14.7                | 8                   | 440.0               | 230                 | 3.23                | 5.345               | 17.42               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Fiat 128            | 32.4                | 4                   |  78.7               |  66                 | 4.08                | 2.200               | 19.47               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Honda Civic         | 30.4                | 4                   |  75.7               |  52                 | 4.93                | 1.615               | 18.52               | 1                   | 1                   | 4                   | 2                   | \n",
       "| Toyota Corolla      | 33.9                | 4                   |  71.1               |  65                 | 4.22                | 1.835               | 19.90               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Toyota Corona       | 21.5                | 4                   | 120.1               |  97                 | 3.70                | 2.465               | 20.01               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Dodge Challenger    | 15.5                | 8                   | 318.0               | 150                 | 2.76                | 3.520               | 16.87               | 0                   | 0                   | 3                   | 2                   | \n",
       "| AMC Javelin         | 15.2                | 8                   | 304.0               | 150                 | 3.15                | 3.435               | 17.30               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Camaro Z28          | 13.3                | 8                   | 350.0               | 245                 | 3.73                | 3.840               | 15.41               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Pontiac Firebird    | 19.2                | 8                   | 400.0               | 175                 | 3.08                | 3.845               | 17.05               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Fiat X1-9           | 27.3                | 4                   |  79.0               |  66                 | 4.08                | 1.935               | 18.90               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Porsche 914-2       | 26.0                | 4                   | 120.3               |  91                 | 4.43                | 2.140               | 16.70               | 0                   | 1                   | 5                   | 2                   | \n",
       "| Lotus Europa        | 30.4                | 4                   |  95.1               | 113                 | 3.77                | 1.513               | 16.90               | 1                   | 1                   | 5                   | 2                   | \n",
       "| Ford Pantera L      | 15.8                | 8                   | 351.0               | 264                 | 4.22                | 3.170               | 14.50               | 0                   | 1                   | 5                   | 4                   | \n",
       "| Ferrari Dino        | 19.7                | 6                   | 145.0               | 175                 | 3.62                | 2.770               | 15.50               | 0                   | 1                   | 5                   | 6                   | \n",
       "| Maserati Bora       | 15.0                | 8                   | 301.0               | 335                 | 3.54                | 3.570               | 14.60               | 0                   | 1                   | 5                   | 8                   | \n",
       "| Volvo 142E          | 21.4                | 4                   | 121.0               | 109                 | 4.11                | 2.780               | 18.60               | 1                   | 1                   | 4                   | 2                   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   car                 mpg  cyl disp  hp  drat wt    qsec  vs am gear carb\n",
       "1  Mazda RX4           21.0 6   160.0 110 3.90 2.620 16.46 0  1  4    4   \n",
       "2  Mazda RX4 Wag       21.0 6   160.0 110 3.90 2.875 17.02 0  1  4    4   \n",
       "3  Datsun 710          22.8 4   108.0  93 3.85 2.320 18.61 1  1  4    1   \n",
       "4  Hornet 4 Drive      21.4 6   258.0 110 3.08 3.215 19.44 1  0  3    1   \n",
       "5  Hornet Sportabout   18.7 8   360.0 175 3.15 3.440 17.02 0  0  3    2   \n",
       "6  Valiant             18.1 6   225.0 105 2.76 3.460 20.22 1  0  3    1   \n",
       "7  Duster 360          14.3 8   360.0 245 3.21 3.570 15.84 0  0  3    4   \n",
       "8  Merc 240D           24.4 4   146.7  62 3.69 3.190 20.00 1  0  4    2   \n",
       "9  Merc 230            22.8 4   140.8  95 3.92 3.150 22.90 1  0  4    2   \n",
       "10 Merc 280            19.2 6   167.6 123 3.92 3.440 18.30 1  0  4    4   \n",
       "11 Merc 280C           17.8 6   167.6 123 3.92 3.440 18.90 1  0  4    4   \n",
       "12 Merc 450SE          16.4 8   275.8 180 3.07 4.070 17.40 0  0  3    3   \n",
       "13 Merc 450SL          17.3 8   275.8 180 3.07 3.730 17.60 0  0  3    3   \n",
       "14 Merc 450SLC         15.2 8   275.8 180 3.07 3.780 18.00 0  0  3    3   \n",
       "15 Cadillac Fleetwood  10.4 8   472.0 205 2.93 5.250 17.98 0  0  3    4   \n",
       "16 Lincoln Continental 10.4 8   460.0 215 3.00 5.424 17.82 0  0  3    4   \n",
       "17 Chrysler Imperial   14.7 8   440.0 230 3.23 5.345 17.42 0  0  3    4   \n",
       "18 Fiat 128            32.4 4    78.7  66 4.08 2.200 19.47 1  1  4    1   \n",
       "19 Honda Civic         30.4 4    75.7  52 4.93 1.615 18.52 1  1  4    2   \n",
       "20 Toyota Corolla      33.9 4    71.1  65 4.22 1.835 19.90 1  1  4    1   \n",
       "21 Toyota Corona       21.5 4   120.1  97 3.70 2.465 20.01 1  0  3    1   \n",
       "22 Dodge Challenger    15.5 8   318.0 150 2.76 3.520 16.87 0  0  3    2   \n",
       "23 AMC Javelin         15.2 8   304.0 150 3.15 3.435 17.30 0  0  3    2   \n",
       "24 Camaro Z28          13.3 8   350.0 245 3.73 3.840 15.41 0  0  3    4   \n",
       "25 Pontiac Firebird    19.2 8   400.0 175 3.08 3.845 17.05 0  0  3    2   \n",
       "26 Fiat X1-9           27.3 4    79.0  66 4.08 1.935 18.90 1  1  4    1   \n",
       "27 Porsche 914-2       26.0 4   120.3  91 4.43 2.140 16.70 0  1  5    2   \n",
       "28 Lotus Europa        30.4 4    95.1 113 3.77 1.513 16.90 1  1  5    2   \n",
       "29 Ford Pantera L      15.8 8   351.0 264 4.22 3.170 14.50 0  1  5    4   \n",
       "30 Ferrari Dino        19.7 6   145.0 175 3.62 2.770 15.50 0  1  5    6   \n",
       "31 Maserati Bora       15.0 8   301.0 335 3.54 3.570 14.60 0  1  5    8   \n",
       "32 Volvo 142E          21.4 4   121.0 109 4.11 2.780 18.60 1  1  4    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dplyr doesn't use row names, so mtcars2 has row\n",
    "# names pulled into a separate column (car)\n",
    "mtcars2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>car</th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Mazda RX4     </td><td>21.0          </td><td>6             </td><td>160.0         </td><td>110           </td><td>3.90          </td><td>2.620         </td><td>16.46         </td><td>0             </td><td>1             </td><td>4             </td><td>4             </td></tr>\n",
       "\t<tr><td>Mazda RX4 Wag </td><td>21.0          </td><td>6             </td><td>160.0         </td><td>110           </td><td>3.90          </td><td>2.875         </td><td>17.02         </td><td>0             </td><td>1             </td><td>4             </td><td>4             </td></tr>\n",
       "\t<tr><td>Datsun 710    </td><td>22.8          </td><td>4             </td><td>108.0         </td><td> 93           </td><td>3.85          </td><td>2.320         </td><td>18.61         </td><td>1             </td><td>1             </td><td>4             </td><td>1             </td></tr>\n",
       "\t<tr><td>Fiat 128      </td><td>32.4          </td><td>4             </td><td> 78.7         </td><td> 66           </td><td>4.08          </td><td>2.200         </td><td>19.47         </td><td>1             </td><td>1             </td><td>4             </td><td>1             </td></tr>\n",
       "\t<tr><td>Honda Civic   </td><td>30.4          </td><td>4             </td><td> 75.7         </td><td> 52           </td><td>4.93          </td><td>1.615         </td><td>18.52         </td><td>1             </td><td>1             </td><td>4             </td><td>2             </td></tr>\n",
       "\t<tr><td>Toyota Corolla</td><td>33.9          </td><td>4             </td><td> 71.1         </td><td> 65           </td><td>4.22          </td><td>1.835         </td><td>19.90         </td><td>1             </td><td>1             </td><td>4             </td><td>1             </td></tr>\n",
       "\t<tr><td>Fiat X1-9     </td><td>27.3          </td><td>4             </td><td> 79.0         </td><td> 66           </td><td>4.08          </td><td>1.935         </td><td>18.90         </td><td>1             </td><td>1             </td><td>4             </td><td>1             </td></tr>\n",
       "\t<tr><td>Volvo 142E    </td><td>21.4          </td><td>4             </td><td>121.0         </td><td>109           </td><td>4.11          </td><td>2.780         </td><td>18.60         </td><td>1             </td><td>1             </td><td>4             </td><td>2             </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllll}\n",
       " car & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n",
       "\\hline\n",
       "\t Mazda RX4      & 21.0           & 6              & 160.0          & 110            & 3.90           & 2.620          & 16.46          & 0              & 1              & 4              & 4             \\\\\n",
       "\t Mazda RX4 Wag  & 21.0           & 6              & 160.0          & 110            & 3.90           & 2.875          & 17.02          & 0              & 1              & 4              & 4             \\\\\n",
       "\t Datsun 710     & 22.8           & 4              & 108.0          &  93            & 3.85           & 2.320          & 18.61          & 1              & 1              & 4              & 1             \\\\\n",
       "\t Fiat 128       & 32.4           & 4              &  78.7          &  66            & 4.08           & 2.200          & 19.47          & 1              & 1              & 4              & 1             \\\\\n",
       "\t Honda Civic    & 30.4           & 4              &  75.7          &  52            & 4.93           & 1.615          & 18.52          & 1              & 1              & 4              & 2             \\\\\n",
       "\t Toyota Corolla & 33.9           & 4              &  71.1          &  65            & 4.22           & 1.835          & 19.90          & 1              & 1              & 4              & 1             \\\\\n",
       "\t Fiat X1-9      & 27.3           & 4              &  79.0          &  66            & 4.08           & 1.935          & 18.90          & 1              & 1              & 4              & 1             \\\\\n",
       "\t Volvo 142E     & 21.4           & 4              & 121.0          & 109            & 4.11           & 2.780          & 18.60          & 1              & 1              & 4              & 2             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "car | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | \n",
       "|---|---|---|---|---|---|---|---|\n",
       "| Mazda RX4      | 21.0           | 6              | 160.0          | 110            | 3.90           | 2.620          | 16.46          | 0              | 1              | 4              | 4              | \n",
       "| Mazda RX4 Wag  | 21.0           | 6              | 160.0          | 110            | 3.90           | 2.875          | 17.02          | 0              | 1              | 4              | 4              | \n",
       "| Datsun 710     | 22.8           | 4              | 108.0          |  93            | 3.85           | 2.320          | 18.61          | 1              | 1              | 4              | 1              | \n",
       "| Fiat 128       | 32.4           | 4              |  78.7          |  66            | 4.08           | 2.200          | 19.47          | 1              | 1              | 4              | 1              | \n",
       "| Honda Civic    | 30.4           | 4              |  75.7          |  52            | 4.93           | 1.615          | 18.52          | 1              | 1              | 4              | 2              | \n",
       "| Toyota Corolla | 33.9           | 4              |  71.1          |  65            | 4.22           | 1.835          | 19.90          | 1              | 1              | 4              | 1              | \n",
       "| Fiat X1-9      | 27.3           | 4              |  79.0          |  66            | 4.08           | 1.935          | 18.90          | 1              | 1              | 4              | 1              | \n",
       "| Volvo 142E     | 21.4           | 4              | 121.0          | 109            | 4.11           | 2.780          | 18.60          | 1              | 1              | 4              | 2              | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  car            mpg  cyl disp  hp  drat wt    qsec  vs am gear carb\n",
       "1 Mazda RX4      21.0 6   160.0 110 3.90 2.620 16.46 0  1  4    4   \n",
       "2 Mazda RX4 Wag  21.0 6   160.0 110 3.90 2.875 17.02 0  1  4    4   \n",
       "3 Datsun 710     22.8 4   108.0  93 3.85 2.320 18.61 1  1  4    1   \n",
       "4 Fiat 128       32.4 4    78.7  66 4.08 2.200 19.47 1  1  4    1   \n",
       "5 Honda Civic    30.4 4    75.7  52 4.93 1.615 18.52 1  1  4    2   \n",
       "6 Toyota Corolla 33.9 4    71.1  65 4.22 1.835 19.90 1  1  4    1   \n",
       "7 Fiat X1-9      27.3 4    79.0  66 4.08 1.935 18.90 1  1  4    1   \n",
       "8 Volvo 142E     21.4 4   121.0 109 4.11 2.780 18.60 1  1  4    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "filter(mtcars2, gear == 4 & am == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>car</th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Volvo 142E         </td><td>21.4               </td><td>4                  </td><td>121.0              </td><td>109                </td><td>4.11               </td><td>2.780              </td><td>18.60              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Toyota Corona      </td><td>21.5               </td><td>4                  </td><td>120.1              </td><td> 97                </td><td>3.70               </td><td>2.465              </td><td>20.01              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Datsun 710         </td><td>22.8               </td><td>4                  </td><td>108.0              </td><td> 93                </td><td>3.85               </td><td>2.320              </td><td>18.61              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Merc 230           </td><td>22.8               </td><td>4                  </td><td>140.8              </td><td> 95                </td><td>3.92               </td><td>3.150              </td><td>22.90              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Merc 240D          </td><td>24.4               </td><td>4                  </td><td>146.7              </td><td> 62                </td><td>3.69               </td><td>3.190              </td><td>20.00              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Porsche 914-2      </td><td>26.0               </td><td>4                  </td><td>120.3              </td><td> 91                </td><td>4.43               </td><td>2.140              </td><td>16.70              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Fiat X1-9          </td><td>27.3               </td><td>4                  </td><td> 79.0              </td><td> 66                </td><td>4.08               </td><td>1.935              </td><td>18.90              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Honda Civic        </td><td>30.4               </td><td>4                  </td><td> 75.7              </td><td> 52                </td><td>4.93               </td><td>1.615              </td><td>18.52              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Lotus Europa       </td><td>30.4               </td><td>4                  </td><td> 95.1              </td><td>113                </td><td>3.77               </td><td>1.513              </td><td>16.90              </td><td>1                  </td><td>1                  </td><td>5                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Fiat 128           </td><td>32.4               </td><td>4                  </td><td> 78.7              </td><td> 66                </td><td>4.08               </td><td>2.200              </td><td>19.47              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Toyota Corolla     </td><td>33.9               </td><td>4                  </td><td> 71.1              </td><td> 65                </td><td>4.22               </td><td>1.835              </td><td>19.90              </td><td>1                  </td><td>1                  </td><td>4                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Merc 280C          </td><td>17.8               </td><td>6                  </td><td>167.6              </td><td>123                </td><td>3.92               </td><td>3.440              </td><td>18.90              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Valiant            </td><td>18.1               </td><td>6                  </td><td>225.0              </td><td>105                </td><td>2.76               </td><td>3.460              </td><td>20.22              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Merc 280           </td><td>19.2               </td><td>6                  </td><td>167.6              </td><td>123                </td><td>3.92               </td><td>3.440              </td><td>18.30              </td><td>1                  </td><td>0                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Ferrari Dino       </td><td>19.7               </td><td>6                  </td><td>145.0              </td><td>175                </td><td>3.62               </td><td>2.770              </td><td>15.50              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>6                  </td></tr>\n",
       "\t<tr><td>Mazda RX4          </td><td>21.0               </td><td>6                  </td><td>160.0              </td><td>110                </td><td>3.90               </td><td>2.620              </td><td>16.46              </td><td>0                  </td><td>1                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Mazda RX4 Wag      </td><td>21.0               </td><td>6                  </td><td>160.0              </td><td>110                </td><td>3.90               </td><td>2.875              </td><td>17.02              </td><td>0                  </td><td>1                  </td><td>4                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Hornet 4 Drive     </td><td>21.4               </td><td>6                  </td><td>258.0              </td><td>110                </td><td>3.08               </td><td>3.215              </td><td>19.44              </td><td>1                  </td><td>0                  </td><td>3                  </td><td>1                  </td></tr>\n",
       "\t<tr><td>Cadillac Fleetwood </td><td>10.4               </td><td>8                  </td><td>472.0              </td><td>205                </td><td>2.93               </td><td>5.250              </td><td>17.98              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Lincoln Continental</td><td>10.4               </td><td>8                  </td><td>460.0              </td><td>215                </td><td>3.00               </td><td>5.424              </td><td>17.82              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Camaro Z28         </td><td>13.3               </td><td>8                  </td><td>350.0              </td><td>245                </td><td>3.73               </td><td>3.840              </td><td>15.41              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Duster 360         </td><td>14.3               </td><td>8                  </td><td>360.0              </td><td>245                </td><td>3.21               </td><td>3.570              </td><td>15.84              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Chrysler Imperial  </td><td>14.7               </td><td>8                  </td><td>440.0              </td><td>230                </td><td>3.23               </td><td>5.345              </td><td>17.42              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Maserati Bora      </td><td>15.0               </td><td>8                  </td><td>301.0              </td><td>335                </td><td>3.54               </td><td>3.570              </td><td>14.60              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>8                  </td></tr>\n",
       "\t<tr><td>Merc 450SLC        </td><td>15.2               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>3.780              </td><td>18.00              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>AMC Javelin        </td><td>15.2               </td><td>8                  </td><td>304.0              </td><td>150                </td><td>3.15               </td><td>3.435              </td><td>17.30              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Dodge Challenger   </td><td>15.5               </td><td>8                  </td><td>318.0              </td><td>150                </td><td>2.76               </td><td>3.520              </td><td>16.87              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Ford Pantera L     </td><td>15.8               </td><td>8                  </td><td>351.0              </td><td>264                </td><td>4.22               </td><td>3.170              </td><td>14.50              </td><td>0                  </td><td>1                  </td><td>5                  </td><td>4                  </td></tr>\n",
       "\t<tr><td>Merc 450SE         </td><td>16.4               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>4.070              </td><td>17.40              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>Merc 450SL         </td><td>17.3               </td><td>8                  </td><td>275.8              </td><td>180                </td><td>3.07               </td><td>3.730              </td><td>17.60              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>3                  </td></tr>\n",
       "\t<tr><td>Hornet Sportabout  </td><td>18.7               </td><td>8                  </td><td>360.0              </td><td>175                </td><td>3.15               </td><td>3.440              </td><td>17.02              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "\t<tr><td>Pontiac Firebird   </td><td>19.2               </td><td>8                  </td><td>400.0              </td><td>175                </td><td>3.08               </td><td>3.845              </td><td>17.05              </td><td>0                  </td><td>0                  </td><td>3                  </td><td>2                  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllll}\n",
       " car & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n",
       "\\hline\n",
       "\t Volvo 142E          & 21.4                & 4                   & 121.0               & 109                 & 4.11                & 2.780               & 18.60               & 1                   & 1                   & 4                   & 2                  \\\\\n",
       "\t Toyota Corona       & 21.5                & 4                   & 120.1               &  97                 & 3.70                & 2.465               & 20.01               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Datsun 710          & 22.8                & 4                   & 108.0               &  93                 & 3.85                & 2.320               & 18.61               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Merc 230            & 22.8                & 4                   & 140.8               &  95                 & 3.92                & 3.150               & 22.90               & 1                   & 0                   & 4                   & 2                  \\\\\n",
       "\t Merc 240D           & 24.4                & 4                   & 146.7               &  62                 & 3.69                & 3.190               & 20.00               & 1                   & 0                   & 4                   & 2                  \\\\\n",
       "\t Porsche 914-2       & 26.0                & 4                   & 120.3               &  91                 & 4.43                & 2.140               & 16.70               & 0                   & 1                   & 5                   & 2                  \\\\\n",
       "\t Fiat X1-9           & 27.3                & 4                   &  79.0               &  66                 & 4.08                & 1.935               & 18.90               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Honda Civic         & 30.4                & 4                   &  75.7               &  52                 & 4.93                & 1.615               & 18.52               & 1                   & 1                   & 4                   & 2                  \\\\\n",
       "\t Lotus Europa        & 30.4                & 4                   &  95.1               & 113                 & 3.77                & 1.513               & 16.90               & 1                   & 1                   & 5                   & 2                  \\\\\n",
       "\t Fiat 128            & 32.4                & 4                   &  78.7               &  66                 & 4.08                & 2.200               & 19.47               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Toyota Corolla      & 33.9                & 4                   &  71.1               &  65                 & 4.22                & 1.835               & 19.90               & 1                   & 1                   & 4                   & 1                  \\\\\n",
       "\t Merc 280C           & 17.8                & 6                   & 167.6               & 123                 & 3.92                & 3.440               & 18.90               & 1                   & 0                   & 4                   & 4                  \\\\\n",
       "\t Valiant             & 18.1                & 6                   & 225.0               & 105                 & 2.76                & 3.460               & 20.22               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Merc 280            & 19.2                & 6                   & 167.6               & 123                 & 3.92                & 3.440               & 18.30               & 1                   & 0                   & 4                   & 4                  \\\\\n",
       "\t Ferrari Dino        & 19.7                & 6                   & 145.0               & 175                 & 3.62                & 2.770               & 15.50               & 0                   & 1                   & 5                   & 6                  \\\\\n",
       "\t Mazda RX4           & 21.0                & 6                   & 160.0               & 110                 & 3.90                & 2.620               & 16.46               & 0                   & 1                   & 4                   & 4                  \\\\\n",
       "\t Mazda RX4 Wag       & 21.0                & 6                   & 160.0               & 110                 & 3.90                & 2.875               & 17.02               & 0                   & 1                   & 4                   & 4                  \\\\\n",
       "\t Hornet 4 Drive      & 21.4                & 6                   & 258.0               & 110                 & 3.08                & 3.215               & 19.44               & 1                   & 0                   & 3                   & 1                  \\\\\n",
       "\t Cadillac Fleetwood  & 10.4                & 8                   & 472.0               & 205                 & 2.93                & 5.250               & 17.98               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Lincoln Continental & 10.4                & 8                   & 460.0               & 215                 & 3.00                & 5.424               & 17.82               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Camaro Z28          & 13.3                & 8                   & 350.0               & 245                 & 3.73                & 3.840               & 15.41               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Duster 360          & 14.3                & 8                   & 360.0               & 245                 & 3.21                & 3.570               & 15.84               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Chrysler Imperial   & 14.7                & 8                   & 440.0               & 230                 & 3.23                & 5.345               & 17.42               & 0                   & 0                   & 3                   & 4                  \\\\\n",
       "\t Maserati Bora       & 15.0                & 8                   & 301.0               & 335                 & 3.54                & 3.570               & 14.60               & 0                   & 1                   & 5                   & 8                  \\\\\n",
       "\t Merc 450SLC         & 15.2                & 8                   & 275.8               & 180                 & 3.07                & 3.780               & 18.00               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t AMC Javelin         & 15.2                & 8                   & 304.0               & 150                 & 3.15                & 3.435               & 17.30               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Dodge Challenger    & 15.5                & 8                   & 318.0               & 150                 & 2.76                & 3.520               & 16.87               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Ford Pantera L      & 15.8                & 8                   & 351.0               & 264                 & 4.22                & 3.170               & 14.50               & 0                   & 1                   & 5                   & 4                  \\\\\n",
       "\t Merc 450SE          & 16.4                & 8                   & 275.8               & 180                 & 3.07                & 4.070               & 17.40               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t Merc 450SL          & 17.3                & 8                   & 275.8               & 180                 & 3.07                & 3.730               & 17.60               & 0                   & 0                   & 3                   & 3                  \\\\\n",
       "\t Hornet Sportabout   & 18.7                & 8                   & 360.0               & 175                 & 3.15                & 3.440               & 17.02               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\t Pontiac Firebird    & 19.2                & 8                   & 400.0               & 175                 & 3.08                & 3.845               & 17.05               & 0                   & 0                   & 3                   & 2                  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "car | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| Volvo 142E          | 21.4                | 4                   | 121.0               | 109                 | 4.11                | 2.780               | 18.60               | 1                   | 1                   | 4                   | 2                   | \n",
       "| Toyota Corona       | 21.5                | 4                   | 120.1               |  97                 | 3.70                | 2.465               | 20.01               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Datsun 710          | 22.8                | 4                   | 108.0               |  93                 | 3.85                | 2.320               | 18.61               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Merc 230            | 22.8                | 4                   | 140.8               |  95                 | 3.92                | 3.150               | 22.90               | 1                   | 0                   | 4                   | 2                   | \n",
       "| Merc 240D           | 24.4                | 4                   | 146.7               |  62                 | 3.69                | 3.190               | 20.00               | 1                   | 0                   | 4                   | 2                   | \n",
       "| Porsche 914-2       | 26.0                | 4                   | 120.3               |  91                 | 4.43                | 2.140               | 16.70               | 0                   | 1                   | 5                   | 2                   | \n",
       "| Fiat X1-9           | 27.3                | 4                   |  79.0               |  66                 | 4.08                | 1.935               | 18.90               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Honda Civic         | 30.4                | 4                   |  75.7               |  52                 | 4.93                | 1.615               | 18.52               | 1                   | 1                   | 4                   | 2                   | \n",
       "| Lotus Europa        | 30.4                | 4                   |  95.1               | 113                 | 3.77                | 1.513               | 16.90               | 1                   | 1                   | 5                   | 2                   | \n",
       "| Fiat 128            | 32.4                | 4                   |  78.7               |  66                 | 4.08                | 2.200               | 19.47               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Toyota Corolla      | 33.9                | 4                   |  71.1               |  65                 | 4.22                | 1.835               | 19.90               | 1                   | 1                   | 4                   | 1                   | \n",
       "| Merc 280C           | 17.8                | 6                   | 167.6               | 123                 | 3.92                | 3.440               | 18.90               | 1                   | 0                   | 4                   | 4                   | \n",
       "| Valiant             | 18.1                | 6                   | 225.0               | 105                 | 2.76                | 3.460               | 20.22               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Merc 280            | 19.2                | 6                   | 167.6               | 123                 | 3.92                | 3.440               | 18.30               | 1                   | 0                   | 4                   | 4                   | \n",
       "| Ferrari Dino        | 19.7                | 6                   | 145.0               | 175                 | 3.62                | 2.770               | 15.50               | 0                   | 1                   | 5                   | 6                   | \n",
       "| Mazda RX4           | 21.0                | 6                   | 160.0               | 110                 | 3.90                | 2.620               | 16.46               | 0                   | 1                   | 4                   | 4                   | \n",
       "| Mazda RX4 Wag       | 21.0                | 6                   | 160.0               | 110                 | 3.90                | 2.875               | 17.02               | 0                   | 1                   | 4                   | 4                   | \n",
       "| Hornet 4 Drive      | 21.4                | 6                   | 258.0               | 110                 | 3.08                | 3.215               | 19.44               | 1                   | 0                   | 3                   | 1                   | \n",
       "| Cadillac Fleetwood  | 10.4                | 8                   | 472.0               | 205                 | 2.93                | 5.250               | 17.98               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Lincoln Continental | 10.4                | 8                   | 460.0               | 215                 | 3.00                | 5.424               | 17.82               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Camaro Z28          | 13.3                | 8                   | 350.0               | 245                 | 3.73                | 3.840               | 15.41               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Duster 360          | 14.3                | 8                   | 360.0               | 245                 | 3.21                | 3.570               | 15.84               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Chrysler Imperial   | 14.7                | 8                   | 440.0               | 230                 | 3.23                | 5.345               | 17.42               | 0                   | 0                   | 3                   | 4                   | \n",
       "| Maserati Bora       | 15.0                | 8                   | 301.0               | 335                 | 3.54                | 3.570               | 14.60               | 0                   | 1                   | 5                   | 8                   | \n",
       "| Merc 450SLC         | 15.2                | 8                   | 275.8               | 180                 | 3.07                | 3.780               | 18.00               | 0                   | 0                   | 3                   | 3                   | \n",
       "| AMC Javelin         | 15.2                | 8                   | 304.0               | 150                 | 3.15                | 3.435               | 17.30               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Dodge Challenger    | 15.5                | 8                   | 318.0               | 150                 | 2.76                | 3.520               | 16.87               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Ford Pantera L      | 15.8                | 8                   | 351.0               | 264                 | 4.22                | 3.170               | 14.50               | 0                   | 1                   | 5                   | 4                   | \n",
       "| Merc 450SE          | 16.4                | 8                   | 275.8               | 180                 | 3.07                | 4.070               | 17.40               | 0                   | 0                   | 3                   | 3                   | \n",
       "| Merc 450SL          | 17.3                | 8                   | 275.8               | 180                 | 3.07                | 3.730               | 17.60               | 0                   | 0                   | 3                   | 3                   | \n",
       "| Hornet Sportabout   | 18.7                | 8                   | 360.0               | 175                 | 3.15                | 3.440               | 17.02               | 0                   | 0                   | 3                   | 2                   | \n",
       "| Pontiac Firebird    | 19.2                | 8                   | 400.0               | 175                 | 3.08                | 3.845               | 17.05               | 0                   | 0                   | 3                   | 2                   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   car                 mpg  cyl disp  hp  drat wt    qsec  vs am gear carb\n",
       "1  Volvo 142E          21.4 4   121.0 109 4.11 2.780 18.60 1  1  4    2   \n",
       "2  Toyota Corona       21.5 4   120.1  97 3.70 2.465 20.01 1  0  3    1   \n",
       "3  Datsun 710          22.8 4   108.0  93 3.85 2.320 18.61 1  1  4    1   \n",
       "4  Merc 230            22.8 4   140.8  95 3.92 3.150 22.90 1  0  4    2   \n",
       "5  Merc 240D           24.4 4   146.7  62 3.69 3.190 20.00 1  0  4    2   \n",
       "6  Porsche 914-2       26.0 4   120.3  91 4.43 2.140 16.70 0  1  5    2   \n",
       "7  Fiat X1-9           27.3 4    79.0  66 4.08 1.935 18.90 1  1  4    1   \n",
       "8  Honda Civic         30.4 4    75.7  52 4.93 1.615 18.52 1  1  4    2   \n",
       "9  Lotus Europa        30.4 4    95.1 113 3.77 1.513 16.90 1  1  5    2   \n",
       "10 Fiat 128            32.4 4    78.7  66 4.08 2.200 19.47 1  1  4    1   \n",
       "11 Toyota Corolla      33.9 4    71.1  65 4.22 1.835 19.90 1  1  4    1   \n",
       "12 Merc 280C           17.8 6   167.6 123 3.92 3.440 18.90 1  0  4    4   \n",
       "13 Valiant             18.1 6   225.0 105 2.76 3.460 20.22 1  0  3    1   \n",
       "14 Merc 280            19.2 6   167.6 123 3.92 3.440 18.30 1  0  4    4   \n",
       "15 Ferrari Dino        19.7 6   145.0 175 3.62 2.770 15.50 0  1  5    6   \n",
       "16 Mazda RX4           21.0 6   160.0 110 3.90 2.620 16.46 0  1  4    4   \n",
       "17 Mazda RX4 Wag       21.0 6   160.0 110 3.90 2.875 17.02 0  1  4    4   \n",
       "18 Hornet 4 Drive      21.4 6   258.0 110 3.08 3.215 19.44 1  0  3    1   \n",
       "19 Cadillac Fleetwood  10.4 8   472.0 205 2.93 5.250 17.98 0  0  3    4   \n",
       "20 Lincoln Continental 10.4 8   460.0 215 3.00 5.424 17.82 0  0  3    4   \n",
       "21 Camaro Z28          13.3 8   350.0 245 3.73 3.840 15.41 0  0  3    4   \n",
       "22 Duster 360          14.3 8   360.0 245 3.21 3.570 15.84 0  0  3    4   \n",
       "23 Chrysler Imperial   14.7 8   440.0 230 3.23 5.345 17.42 0  0  3    4   \n",
       "24 Maserati Bora       15.0 8   301.0 335 3.54 3.570 14.60 0  1  5    8   \n",
       "25 Merc 450SLC         15.2 8   275.8 180 3.07 3.780 18.00 0  0  3    3   \n",
       "26 AMC Javelin         15.2 8   304.0 150 3.15 3.435 17.30 0  0  3    2   \n",
       "27 Dodge Challenger    15.5 8   318.0 150 2.76 3.520 16.87 0  0  3    2   \n",
       "28 Ford Pantera L      15.8 8   351.0 264 4.22 3.170 14.50 0  1  5    4   \n",
       "29 Merc 450SE          16.4 8   275.8 180 3.07 4.070 17.40 0  0  3    3   \n",
       "30 Merc 450SL          17.3 8   275.8 180 3.07 3.730 17.60 0  0  3    3   \n",
       "31 Hornet Sportabout   18.7 8   360.0 175 3.15 3.440 17.02 0  0  3    2   \n",
       "32 Pontiac Firebird    19.2 8   400.0 175 3.08 3.845 17.05 0  0  3    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "arrange(mtcars2, cyl, mpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>car</th><th scope=col>pw</th><th scope=col>mpg</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Maserati Bora </td><td>93.83754      </td><td>15.0          </td></tr>\n",
       "\t<tr><td>Ford Pantera L</td><td>83.28076      </td><td>15.8          </td></tr>\n",
       "\t<tr><td>Lotus Europa  </td><td>74.68605      </td><td>30.4          </td></tr>\n",
       "\t<tr><td>Duster 360    </td><td>68.62745      </td><td>14.3          </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " car & pw & mpg\\\\\n",
       "\\hline\n",
       "\t Maserati Bora  & 93.83754       & 15.0          \\\\\n",
       "\t Ford Pantera L & 83.28076       & 15.8          \\\\\n",
       "\t Lotus Europa   & 74.68605       & 30.4          \\\\\n",
       "\t Duster 360     & 68.62745       & 14.3          \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "car | pw | mpg | \n",
       "|---|---|---|---|\n",
       "| Maserati Bora  | 93.83754       | 15.0           | \n",
       "| Ford Pantera L | 83.28076       | 15.8           | \n",
       "| Lotus Europa   | 74.68605       | 30.4           | \n",
       "| Duster 360     | 68.62745       | 14.3           | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  car            pw       mpg \n",
       "1 Maserati Bora  93.83754 15.0\n",
       "2 Ford Pantera L 83.28076 15.8\n",
       "3 Lotus Europa   74.68605 30.4\n",
       "4 Duster 360     68.62745 14.3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "transform(mtcars2, pw = hp / wt) %>% arrange(-pw) %>% select(car, pw, mpg) %>% slice(1:4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>cyl</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>6</td></tr>\n",
       "\t<tr><td>4</td></tr>\n",
       "\t<tr><td>8</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       " cyl\\\\\n",
       "\\hline\n",
       "\t 6\\\\\n",
       "\t 4\\\\\n",
       "\t 8\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "cyl | \n",
       "|---|---|---|\n",
       "| 6 | \n",
       "| 4 | \n",
       "| 8 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  cyl\n",
       "1 6  \n",
       "2 4  \n",
       "3 8  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distinct(mtcars2, cyl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>cyl</th><th scope=col>count</th><th scope=col>avg_mpg</th><th scope=col>avg_hp</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>4        </td><td>11       </td><td>26.66364 </td><td> 82.63636</td></tr>\n",
       "\t<tr><td>6        </td><td> 7       </td><td>19.74286 </td><td>122.28571</td></tr>\n",
       "\t<tr><td>8        </td><td>14       </td><td>15.10000 </td><td>209.21429</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " cyl & count & avg\\_mpg & avg\\_hp\\\\\n",
       "\\hline\n",
       "\t 4         & 11        & 26.66364  &  82.63636\\\\\n",
       "\t 6         &  7        & 19.74286  & 122.28571\\\\\n",
       "\t 8         & 14        & 15.10000  & 209.21429\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "cyl | count | avg_mpg | avg_hp | \n",
       "|---|---|---|\n",
       "| 4         | 11        | 26.66364  |  82.63636 | \n",
       "| 6         |  7        | 19.74286  | 122.28571 | \n",
       "| 8         | 14        | 15.10000  | 209.21429 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  cyl count avg_mpg  avg_hp   \n",
       "1 4   11    26.66364  82.63636\n",
       "2 6    7    19.74286 122.28571\n",
       "3 8   14    15.10000 209.21429"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "group_by(mtcars2, cyl) %>% summarise(count = n(), avg_mpg = mean(mpg), avg_hp = mean(hp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OnTv/rqqyNHjgghjhw58umnn86cObPVn05V1YyMjMAjI4liBwAA2iExMXHPnj1L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\nCIRgBwAQCMEOACAQgh0AQCAEOwCAQPw/dE4Xw8gn0O0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "ggplot(mtcars2, aes(x = hp, y=mpg)) + geom_point(aes(colour = as.factor(cyl)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading a \"real\" dataset from a CSV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "letters <- read.table(\"letter-recognition.data\", sep=\",\", header=FALSE);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "colnames(letters) <- c(\"Letter\", \"Xbox\", \"Ybox\", \"Width\", \"Height\",\n",
    "                       \"OnPix\", \"Xbar\", \"Ybar\", \"X2bar\", \"Y2bar\",\n",
    "                       \"XYbar\", \"X2Ybar\", \"XY2bar\", \"Xedge\",\n",
    "                       \"XedgeXY\", \"Yedge\", \"YedgeYX\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>20000</li>\n",
       "\t<li>17</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 20000\n",
       "\\item 17\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 20000\n",
       "2. 17\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 20000    17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(letters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Remove labels, standardize results to mean 0/stdev 1 (slides explain why)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(dplyr)\n",
    "mtx <- scale(select(letters, -Letter))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Xbox</th><th scope=col>Ybox</th><th scope=col>Width</th><th scope=col>Height</th><th scope=col>OnPix</th><th scope=col>Xbar</th><th scope=col>Ybar</th><th scope=col>X2bar</th><th scope=col>Y2bar</th><th scope=col>XYbar</th><th scope=col>X2Ybar</th><th scope=col>XY2bar</th><th scope=col>Xedge</th><th scope=col>XedgeXY</th><th scope=col>Yedge</th><th scope=col>YedgeYX</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>-1.05767185</td><td> 0.2918698 </td><td>-1.05325034</td><td>-0.1646996 </td><td>-1.1439846 </td><td> 0.5441168 </td><td> 2.3650380 </td><td>-1.7143167 </td><td> 0.3449858 </td><td>-0.9170476 </td><td> 1.3477406 </td><td> 0.03412446</td><td>-1.30591496</td><td>-0.2190762 </td><td>-1.4381167 </td><td> 0.1229080 </td></tr>\n",
       "\t<tr><td> 0.51037221</td><td> 1.5023201 </td><td>-1.05325034</td><td> 0.7197121 </td><td>-0.6874590 </td><td> 1.5312664 </td><td>-1.0752987 </td><td> 0.1375572 </td><td>-0.4950599 </td><td> 1.8959203 </td><td>-1.3127738 </td><td> 0.51475066</td><td>-0.44848089</td><td>-0.2190762 </td><td> 0.1200784 </td><td> 1.3594069 </td></tr>\n",
       "\t<tr><td>-0.01230915</td><td> 1.1997076 </td><td> 0.43589876</td><td> 1.1619179 </td><td> 1.1386432 </td><td> 1.5312664 </td><td>-0.6452567 </td><td>-0.9735671 </td><td> 0.3449858 </td><td> 0.6903626 </td><td>-1.3127738 </td><td>-0.44650174</td><td>-0.01976386</td><td>-0.8656046 </td><td>-0.2694704 </td><td> 0.7411575 </td></tr>\n",
       "\t<tr><td> 1.55573491</td><td> 1.1997076 </td><td> 0.43589876</td><td> 0.2775063 </td><td>-0.2309335 </td><td>-0.9366075 </td><td> 0.6448696 </td><td>-0.2328176 </td><td> 0.3449858 </td><td>-1.7207527 </td><td>-0.9327003 </td><td> 0.99537685</td><td> 1.26638725</td><td> 1.0739807 </td><td>-0.6590192 </td><td> 0.1229080 </td></tr>\n",
       "\t<tr><td>-1.05767185</td><td>-1.8264182 </td><td>-1.05325034</td><td>-1.9335228 </td><td>-1.1439846 </td><td> 0.5441168 </td><td>-0.6452567 </td><td> 0.5079320 </td><td> 0.3449858 </td><td>-0.9170476 </td><td>-0.5526268 </td><td> 0.51475066</td><td>-0.87719793</td><td>-0.8656046 </td><td> 0.5096272 </td><td> 1.3594069 </td></tr>\n",
       "\t<tr><td>-0.01230915</td><td> 1.1997076 </td><td>-0.06048427</td><td> 1.1619179 </td><td>-0.2309335 </td><td> 0.5441168 </td><td> 0.2148275 </td><td> 0.5079320 </td><td> 1.6050543 </td><td>-1.3189002 </td><td>-0.1725534 </td><td>-0.92712793</td><td>-1.30591496</td><td>-0.2190762 </td><td> 2.0678224 </td><td>-0.4953415 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllll}\n",
       " Xbox & Ybox & Width & Height & OnPix & Xbar & Ybar & X2bar & Y2bar & XYbar & X2Ybar & XY2bar & Xedge & XedgeXY & Yedge & YedgeYX\\\\\n",
       "\\hline\n",
       "\t -1.05767185 &  0.2918698  & -1.05325034 & -0.1646996  & -1.1439846  &  0.5441168  &  2.3650380  & -1.7143167  &  0.3449858  & -0.9170476  &  1.3477406  &  0.03412446 & -1.30591496 & -0.2190762  & -1.4381167  &  0.1229080 \\\\\n",
       "\t  0.51037221 &  1.5023201  & -1.05325034 &  0.7197121  & -0.6874590  &  1.5312664  & -1.0752987  &  0.1375572  & -0.4950599  &  1.8959203  & -1.3127738  &  0.51475066 & -0.44848089 & -0.2190762  &  0.1200784  &  1.3594069 \\\\\n",
       "\t -0.01230915 &  1.1997076  &  0.43589876 &  1.1619179  &  1.1386432  &  1.5312664  & -0.6452567  & -0.9735671  &  0.3449858  &  0.6903626  & -1.3127738  & -0.44650174 & -0.01976386 & -0.8656046  & -0.2694704  &  0.7411575 \\\\\n",
       "\t  1.55573491 &  1.1997076  &  0.43589876 &  0.2775063  & -0.2309335  & -0.9366075  &  0.6448696  & -0.2328176  &  0.3449858  & -1.7207527  & -0.9327003  &  0.99537685 &  1.26638725 &  1.0739807  & -0.6590192  &  0.1229080 \\\\\n",
       "\t -1.05767185 & -1.8264182  & -1.05325034 & -1.9335228  & -1.1439846  &  0.5441168  & -0.6452567  &  0.5079320  &  0.3449858  & -0.9170476  & -0.5526268  &  0.51475066 & -0.87719793 & -0.8656046  &  0.5096272  &  1.3594069 \\\\\n",
       "\t -0.01230915 &  1.1997076  & -0.06048427 &  1.1619179  & -0.2309335  &  0.5441168  &  0.2148275  &  0.5079320  &  1.6050543  & -1.3189002  & -0.1725534  & -0.92712793 & -1.30591496 & -0.2190762  &  2.0678224  & -0.4953415 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Xbox | Ybox | Width | Height | OnPix | Xbar | Ybar | X2bar | Y2bar | XYbar | X2Ybar | XY2bar | Xedge | XedgeXY | Yedge | YedgeYX | \n",
       "|---|---|---|---|---|---|\n",
       "| -1.05767185 |  0.2918698  | -1.05325034 | -0.1646996  | -1.1439846  |  0.5441168  |  2.3650380  | -1.7143167  |  0.3449858  | -0.9170476  |  1.3477406  |  0.03412446 | -1.30591496 | -0.2190762  | -1.4381167  |  0.1229080  | \n",
       "|  0.51037221 |  1.5023201  | -1.05325034 |  0.7197121  | -0.6874590  |  1.5312664  | -1.0752987  |  0.1375572  | -0.4950599  |  1.8959203  | -1.3127738  |  0.51475066 | -0.44848089 | -0.2190762  |  0.1200784  |  1.3594069  | \n",
       "| -0.01230915 |  1.1997076  |  0.43589876 |  1.1619179  |  1.1386432  |  1.5312664  | -0.6452567  | -0.9735671  |  0.3449858  |  0.6903626  | -1.3127738  | -0.44650174 | -0.01976386 | -0.8656046  | -0.2694704  |  0.7411575  | \n",
       "|  1.55573491 |  1.1997076  |  0.43589876 |  0.2775063  | -0.2309335  | -0.9366075  |  0.6448696  | -0.2328176  |  0.3449858  | -1.7207527  | -0.9327003  |  0.99537685 |  1.26638725 |  1.0739807  | -0.6590192  |  0.1229080  | \n",
       "| -1.05767185 | -1.8264182  | -1.05325034 | -1.9335228  | -1.1439846  |  0.5441168  | -0.6452567  |  0.5079320  |  0.3449858  | -0.9170476  | -0.5526268  |  0.51475066 | -0.87719793 | -0.8656046  |  0.5096272  |  1.3594069  | \n",
       "| -0.01230915 |  1.1997076  | -0.06048427 |  1.1619179  | -0.2309335  |  0.5441168  |  0.2148275  |  0.5079320  |  1.6050543  | -1.3189002  | -0.1725534  | -0.92712793 | -1.30591496 | -0.2190762  |  2.0678224  | -0.4953415  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Xbox        Ybox       Width       Height     OnPix      Xbar      \n",
       "[1,] -1.05767185  0.2918698 -1.05325034 -0.1646996 -1.1439846  0.5441168\n",
       "[2,]  0.51037221  1.5023201 -1.05325034  0.7197121 -0.6874590  1.5312664\n",
       "[3,] -0.01230915  1.1997076  0.43589876  1.1619179  1.1386432  1.5312664\n",
       "[4,]  1.55573491  1.1997076  0.43589876  0.2775063 -0.2309335 -0.9366075\n",
       "[5,] -1.05767185 -1.8264182 -1.05325034 -1.9335228 -1.1439846  0.5441168\n",
       "[6,] -0.01230915  1.1997076 -0.06048427  1.1619179 -0.2309335  0.5441168\n",
       "     Ybar       X2bar      Y2bar      XYbar      X2Ybar     XY2bar     \n",
       "[1,]  2.3650380 -1.7143167  0.3449858 -0.9170476  1.3477406  0.03412446\n",
       "[2,] -1.0752987  0.1375572 -0.4950599  1.8959203 -1.3127738  0.51475066\n",
       "[3,] -0.6452567 -0.9735671  0.3449858  0.6903626 -1.3127738 -0.44650174\n",
       "[4,]  0.6448696 -0.2328176  0.3449858 -1.7207527 -0.9327003  0.99537685\n",
       "[5,] -0.6452567  0.5079320  0.3449858 -0.9170476 -0.5526268  0.51475066\n",
       "[6,]  0.2148275  0.5079320  1.6050543 -1.3189002 -0.1725534 -0.92712793\n",
       "     Xedge       XedgeXY    Yedge      YedgeYX   \n",
       "[1,] -1.30591496 -0.2190762 -1.4381167  0.1229080\n",
       "[2,] -0.44848089 -0.2190762  0.1200784  1.3594069\n",
       "[3,] -0.01976386 -0.8656046 -0.2694704  0.7411575\n",
       "[4,]  1.26638725  1.0739807 -0.6590192  0.1229080\n",
       "[5,] -0.87719793 -0.8656046  0.5096272  1.3594069\n",
       "[6,] -1.30591496 -0.2190762  2.0678224 -0.4953415"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(mtx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## Compute covariance matrix (the more explicit way)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cm <- (t(mtx) %*% mtx) /(nrow(mtx) + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Xbox</th><th scope=col>Ybox</th><th scope=col>Width</th><th scope=col>Height</th><th scope=col>OnPix</th><th scope=col>Xbar</th><th scope=col>Ybar</th><th scope=col>X2bar</th><th scope=col>Y2bar</th><th scope=col>XYbar</th><th scope=col>X2Ybar</th><th scope=col>XY2bar</th><th scope=col>Xedge</th><th scope=col>XedgeXY</th><th scope=col>Yedge</th><th scope=col>YedgeYX</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Xbox</th><td> 0.99990</td><td> 0.75772</td><td> 0.85143</td><td> 0.67270</td><td> 0.61903</td><td>-0.03259</td><td> 0.04554</td><td> 0.01430</td><td> 0.05208</td><td> 0.14804</td><td> 0.03546</td><td>-0.04633</td><td> 0.48911</td><td> 0.09817</td><td> 0.27348</td><td>-0.10514</td></tr>\n",
       "\t<tr><th scope=row>Ybox</th><td> 0.75772</td><td> 0.99990</td><td> 0.67184</td><td> 0.82312</td><td> 0.55501</td><td> 0.04569</td><td>-0.04092</td><td>-0.02502</td><td> 0.09647</td><td> 0.15994</td><td>-0.05464</td><td>-0.00757</td><td> 0.27440</td><td>-0.00134</td><td> 0.23086</td><td>-0.04274</td></tr>\n",
       "\t<tr><th scope=row>Width</th><td> 0.85143</td><td> 0.67184</td><td> 0.99990</td><td> 0.66015</td><td> 0.76564</td><td> 0.06195</td><td> 0.02483</td><td>-0.09860</td><td> 0.05707</td><td> 0.11501</td><td> 0.01169</td><td>-0.04500</td><td> 0.55720</td><td> 0.04565</td><td> 0.26026</td><td>-0.11826</td></tr>\n",
       "\t<tr><th scope=row>Height</th><td> 0.67270</td><td> 0.82312</td><td> 0.66015</td><td> 0.99990</td><td> 0.64430</td><td> 0.04284</td><td>-0.02007</td><td> 0.08237</td><td> 0.05903</td><td> 0.01246</td><td>-0.01199</td><td> 0.02638</td><td> 0.26522</td><td> 0.02536</td><td> 0.29752</td><td>-0.01885</td></tr>\n",
       "\t<tr><th scope=row>OnPix</th><td> 0.61903</td><td> 0.55501</td><td> 0.76564</td><td> 0.64430</td><td> 0.99990</td><td> 0.13915</td><td>-0.02882</td><td>-0.01198</td><td>-0.06555</td><td>-0.06977</td><td>-0.07293</td><td>-0.03885</td><td> 0.62744</td><td> 0.01765</td><td> 0.49260</td><td>-0.06296</td></tr>\n",
       "\t<tr><th scope=row>Xbar</th><td>-0.03259</td><td> 0.04569</td><td> 0.06195</td><td> 0.04284</td><td> 0.13915</td><td> 0.99990</td><td>-0.35654</td><td>-0.05330</td><td>-0.12284</td><td> 0.08595</td><td>-0.34192</td><td>-0.03211</td><td> 0.14431</td><td>-0.25331</td><td> 0.12704</td><td> 0.24879</td></tr>\n",
       "\t<tr><th scope=row>Ybar</th><td> 0.04554</td><td>-0.04092</td><td> 0.02483</td><td>-0.02007</td><td>-0.02882</td><td>-0.35654</td><td> 0.99990</td><td>-0.11861</td><td>-0.04965</td><td> 0.17830</td><td> 0.60034</td><td>-0.27162</td><td>-0.03672</td><td> 0.55500</td><td>-0.07800</td><td>-0.20788</td></tr>\n",
       "\t<tr><th scope=row>X2bar</th><td> 0.01430</td><td>-0.02502</td><td>-0.09860</td><td> 0.08237</td><td>-0.01198</td><td>-0.05330</td><td>-0.11861</td><td> 0.99990</td><td>-0.18841</td><td>-0.31775</td><td> 0.04254</td><td> 0.08201</td><td> 0.14212</td><td>-0.08481</td><td> 0.00655</td><td> 0.18288</td></tr>\n",
       "\t<tr><th scope=row>Y2bar</th><td> 0.05208</td><td> 0.09647</td><td> 0.05707</td><td> 0.05903</td><td>-0.06555</td><td>-0.12284</td><td>-0.04965</td><td>-0.18841</td><td> 0.99990</td><td> 0.13199</td><td>-0.06011</td><td> 0.11904</td><td>-0.38398</td><td>-0.05254</td><td> 0.27751</td><td>-0.06133</td></tr>\n",
       "\t<tr><th scope=row>XYbar</th><td> 0.14804</td><td> 0.15994</td><td> 0.11501</td><td> 0.01246</td><td>-0.06977</td><td> 0.08595</td><td> 0.17830</td><td>-0.31775</td><td> 0.13199</td><td> 0.99990</td><td> 0.05798</td><td>-0.10675</td><td>-0.17566</td><td> 0.02942</td><td>-0.08701</td><td>-0.11421</td></tr>\n",
       "\t<tr><th scope=row>X2Ybar</th><td> 0.03546</td><td>-0.05464</td><td> 0.01169</td><td>-0.01199</td><td>-0.07293</td><td>-0.34192</td><td> 0.60034</td><td> 0.04254</td><td>-0.06011</td><td> 0.05798</td><td> 0.99990</td><td> 0.06321</td><td> 0.05356</td><td> 0.52719</td><td>-0.22623</td><td>-0.23649</td></tr>\n",
       "\t<tr><th scope=row>XY2bar</th><td>-0.04633</td><td>-0.00757</td><td>-0.04500</td><td> 0.02638</td><td>-0.03885</td><td>-0.03211</td><td>-0.27162</td><td> 0.08201</td><td> 0.11904</td><td>-0.10675</td><td> 0.06321</td><td> 0.99990</td><td>-0.00875</td><td>-0.18491</td><td> 0.04969</td><td> 0.24578</td></tr>\n",
       "\t<tr><th scope=row>Xedge</th><td> 0.48911</td><td> 0.27440</td><td> 0.55720</td><td> 0.26522</td><td> 0.62744</td><td> 0.14431</td><td>-0.03672</td><td> 0.14212</td><td>-0.38398</td><td>-0.17566</td><td> 0.05356</td><td>-0.00875</td><td> 0.99990</td><td> 0.00285</td><td> 0.10840</td><td>-0.04978</td></tr>\n",
       "\t<tr><th scope=row>XedgeXY</th><td> 0.09817</td><td>-0.00134</td><td> 0.04565</td><td> 0.02536</td><td> 0.01765</td><td>-0.25331</td><td> 0.55500</td><td>-0.08481</td><td>-0.05254</td><td> 0.02942</td><td> 0.52719</td><td>-0.18491</td><td> 0.00285</td><td> 0.99990</td><td>-0.06440</td><td>-0.18757</td></tr>\n",
       "\t<tr><th scope=row>Yedge</th><td> 0.27348</td><td> 0.23086</td><td> 0.26026</td><td> 0.29752</td><td> 0.49260</td><td> 0.12704</td><td>-0.07800</td><td> 0.00655</td><td> 0.27751</td><td>-0.08701</td><td>-0.22623</td><td> 0.04969</td><td> 0.10840</td><td>-0.06440</td><td> 0.99990</td><td> 0.14357</td></tr>\n",
       "\t<tr><th scope=row>YedgeYX</th><td>-0.10514</td><td>-0.04274</td><td>-0.11826</td><td>-0.01885</td><td>-0.06296</td><td> 0.24879</td><td>-0.20788</td><td> 0.18288</td><td>-0.06133</td><td>-0.11421</td><td>-0.23649</td><td> 0.24578</td><td>-0.04978</td><td>-0.18757</td><td> 0.14357</td><td> 0.99990</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllll}\n",
       "  & Xbox & Ybox & Width & Height & OnPix & Xbar & Ybar & X2bar & Y2bar & XYbar & X2Ybar & XY2bar & Xedge & XedgeXY & Yedge & YedgeYX\\\\\n",
       "\\hline\n",
       "\tXbox &  0.99990 &  0.75772 &  0.85143 &  0.67270 &  0.61903 & -0.03259 &  0.04554 &  0.01430 &  0.05208 &  0.14804 &  0.03546 & -0.04633 &  0.48911 &  0.09817 &  0.27348 & -0.10514\\\\\n",
       "\tYbox &  0.75772 &  0.99990 &  0.67184 &  0.82312 &  0.55501 &  0.04569 & -0.04092 & -0.02502 &  0.09647 &  0.15994 & -0.05464 & -0.00757 &  0.27440 & -0.00134 &  0.23086 & -0.04274\\\\\n",
       "\tWidth &  0.85143 &  0.67184 &  0.99990 &  0.66015 &  0.76564 &  0.06195 &  0.02483 & -0.09860 &  0.05707 &  0.11501 &  0.01169 & -0.04500 &  0.55720 &  0.04565 &  0.26026 & -0.11826\\\\\n",
       "\tHeight &  0.67270 &  0.82312 &  0.66015 &  0.99990 &  0.64430 &  0.04284 & -0.02007 &  0.08237 &  0.05903 &  0.01246 & -0.01199 &  0.02638 &  0.26522 &  0.02536 &  0.29752 & -0.01885\\\\\n",
       "\tOnPix &  0.61903 &  0.55501 &  0.76564 &  0.64430 &  0.99990 &  0.13915 & -0.02882 & -0.01198 & -0.06555 & -0.06977 & -0.07293 & -0.03885 &  0.62744 &  0.01765 &  0.49260 & -0.06296\\\\\n",
       "\tXbar & -0.03259 &  0.04569 &  0.06195 &  0.04284 &  0.13915 &  0.99990 & -0.35654 & -0.05330 & -0.12284 &  0.08595 & -0.34192 & -0.03211 &  0.14431 & -0.25331 &  0.12704 &  0.24879\\\\\n",
       "\tYbar &  0.04554 & -0.04092 &  0.02483 & -0.02007 & -0.02882 & -0.35654 &  0.99990 & -0.11861 & -0.04965 &  0.17830 &  0.60034 & -0.27162 & -0.03672 &  0.55500 & -0.07800 & -0.20788\\\\\n",
       "\tX2bar &  0.01430 & -0.02502 & -0.09860 &  0.08237 & -0.01198 & -0.05330 & -0.11861 &  0.99990 & -0.18841 & -0.31775 &  0.04254 &  0.08201 &  0.14212 & -0.08481 &  0.00655 &  0.18288\\\\\n",
       "\tY2bar &  0.05208 &  0.09647 &  0.05707 &  0.05903 & -0.06555 & -0.12284 & -0.04965 & -0.18841 &  0.99990 &  0.13199 & -0.06011 &  0.11904 & -0.38398 & -0.05254 &  0.27751 & -0.06133\\\\\n",
       "\tXYbar &  0.14804 &  0.15994 &  0.11501 &  0.01246 & -0.06977 &  0.08595 &  0.17830 & -0.31775 &  0.13199 &  0.99990 &  0.05798 & -0.10675 & -0.17566 &  0.02942 & -0.08701 & -0.11421\\\\\n",
       "\tX2Ybar &  0.03546 & -0.05464 &  0.01169 & -0.01199 & -0.07293 & -0.34192 &  0.60034 &  0.04254 & -0.06011 &  0.05798 &  0.99990 &  0.06321 &  0.05356 &  0.52719 & -0.22623 & -0.23649\\\\\n",
       "\tXY2bar & -0.04633 & -0.00757 & -0.04500 &  0.02638 & -0.03885 & -0.03211 & -0.27162 &  0.08201 &  0.11904 & -0.10675 &  0.06321 &  0.99990 & -0.00875 & -0.18491 &  0.04969 &  0.24578\\\\\n",
       "\tXedge &  0.48911 &  0.27440 &  0.55720 &  0.26522 &  0.62744 &  0.14431 & -0.03672 &  0.14212 & -0.38398 & -0.17566 &  0.05356 & -0.00875 &  0.99990 &  0.00285 &  0.10840 & -0.04978\\\\\n",
       "\tXedgeXY &  0.09817 & -0.00134 &  0.04565 &  0.02536 &  0.01765 & -0.25331 &  0.55500 & -0.08481 & -0.05254 &  0.02942 &  0.52719 & -0.18491 &  0.00285 &  0.99990 & -0.06440 & -0.18757\\\\\n",
       "\tYedge &  0.27348 &  0.23086 &  0.26026 &  0.29752 &  0.49260 &  0.12704 & -0.07800 &  0.00655 &  0.27751 & -0.08701 & -0.22623 &  0.04969 &  0.10840 & -0.06440 &  0.99990 &  0.14357\\\\\n",
       "\tYedgeYX & -0.10514 & -0.04274 & -0.11826 & -0.01885 & -0.06296 &  0.24879 & -0.20788 &  0.18288 & -0.06133 & -0.11421 & -0.23649 &  0.24578 & -0.04978 & -0.18757 &  0.14357 &  0.99990\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Xbox | Ybox | Width | Height | OnPix | Xbar | Ybar | X2bar | Y2bar | XYbar | X2Ybar | XY2bar | Xedge | XedgeXY | Yedge | YedgeYX | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| Xbox |  0.99990 |  0.75772 |  0.85143 |  0.67270 |  0.61903 | -0.03259 |  0.04554 |  0.01430 |  0.05208 |  0.14804 |  0.03546 | -0.04633 |  0.48911 |  0.09817 |  0.27348 | -0.10514 | \n",
       "| Ybox |  0.75772 |  0.99990 |  0.67184 |  0.82312 |  0.55501 |  0.04569 | -0.04092 | -0.02502 |  0.09647 |  0.15994 | -0.05464 | -0.00757 |  0.27440 | -0.00134 |  0.23086 | -0.04274 | \n",
       "| Width |  0.85143 |  0.67184 |  0.99990 |  0.66015 |  0.76564 |  0.06195 |  0.02483 | -0.09860 |  0.05707 |  0.11501 |  0.01169 | -0.04500 |  0.55720 |  0.04565 |  0.26026 | -0.11826 | \n",
       "| Height |  0.67270 |  0.82312 |  0.66015 |  0.99990 |  0.64430 |  0.04284 | -0.02007 |  0.08237 |  0.05903 |  0.01246 | -0.01199 |  0.02638 |  0.26522 |  0.02536 |  0.29752 | -0.01885 | \n",
       "| OnPix |  0.61903 |  0.55501 |  0.76564 |  0.64430 |  0.99990 |  0.13915 | -0.02882 | -0.01198 | -0.06555 | -0.06977 | -0.07293 | -0.03885 |  0.62744 |  0.01765 |  0.49260 | -0.06296 | \n",
       "| Xbar | -0.03259 |  0.04569 |  0.06195 |  0.04284 |  0.13915 |  0.99990 | -0.35654 | -0.05330 | -0.12284 |  0.08595 | -0.34192 | -0.03211 |  0.14431 | -0.25331 |  0.12704 |  0.24879 | \n",
       "| Ybar |  0.04554 | -0.04092 |  0.02483 | -0.02007 | -0.02882 | -0.35654 |  0.99990 | -0.11861 | -0.04965 |  0.17830 |  0.60034 | -0.27162 | -0.03672 |  0.55500 | -0.07800 | -0.20788 | \n",
       "| X2bar |  0.01430 | -0.02502 | -0.09860 |  0.08237 | -0.01198 | -0.05330 | -0.11861 |  0.99990 | -0.18841 | -0.31775 |  0.04254 |  0.08201 |  0.14212 | -0.08481 |  0.00655 |  0.18288 | \n",
       "| Y2bar |  0.05208 |  0.09647 |  0.05707 |  0.05903 | -0.06555 | -0.12284 | -0.04965 | -0.18841 |  0.99990 |  0.13199 | -0.06011 |  0.11904 | -0.38398 | -0.05254 |  0.27751 | -0.06133 | \n",
       "| XYbar |  0.14804 |  0.15994 |  0.11501 |  0.01246 | -0.06977 |  0.08595 |  0.17830 | -0.31775 |  0.13199 |  0.99990 |  0.05798 | -0.10675 | -0.17566 |  0.02942 | -0.08701 | -0.11421 | \n",
       "| X2Ybar |  0.03546 | -0.05464 |  0.01169 | -0.01199 | -0.07293 | -0.34192 |  0.60034 |  0.04254 | -0.06011 |  0.05798 |  0.99990 |  0.06321 |  0.05356 |  0.52719 | -0.22623 | -0.23649 | \n",
       "| XY2bar | -0.04633 | -0.00757 | -0.04500 |  0.02638 | -0.03885 | -0.03211 | -0.27162 |  0.08201 |  0.11904 | -0.10675 |  0.06321 |  0.99990 | -0.00875 | -0.18491 |  0.04969 |  0.24578 | \n",
       "| Xedge |  0.48911 |  0.27440 |  0.55720 |  0.26522 |  0.62744 |  0.14431 | -0.03672 |  0.14212 | -0.38398 | -0.17566 |  0.05356 | -0.00875 |  0.99990 |  0.00285 |  0.10840 | -0.04978 | \n",
       "| XedgeXY |  0.09817 | -0.00134 |  0.04565 |  0.02536 |  0.01765 | -0.25331 |  0.55500 | -0.08481 | -0.05254 |  0.02942 |  0.52719 | -0.18491 |  0.00285 |  0.99990 | -0.06440 | -0.18757 | \n",
       "| Yedge |  0.27348 |  0.23086 |  0.26026 |  0.29752 |  0.49260 |  0.12704 | -0.07800 |  0.00655 |  0.27751 | -0.08701 | -0.22623 |  0.04969 |  0.10840 | -0.06440 |  0.99990 |  0.14357 | \n",
       "| YedgeYX | -0.10514 | -0.04274 | -0.11826 | -0.01885 | -0.06296 |  0.24879 | -0.20788 |  0.18288 | -0.06133 | -0.11421 | -0.23649 |  0.24578 | -0.04978 | -0.18757 |  0.14357 |  0.99990 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "        Xbox     Ybox     Width    Height   OnPix    Xbar     Ybar     X2bar   \n",
       "Xbox     0.99990  0.75772  0.85143  0.67270  0.61903 -0.03259  0.04554  0.01430\n",
       "Ybox     0.75772  0.99990  0.67184  0.82312  0.55501  0.04569 -0.04092 -0.02502\n",
       "Width    0.85143  0.67184  0.99990  0.66015  0.76564  0.06195  0.02483 -0.09860\n",
       "Height   0.67270  0.82312  0.66015  0.99990  0.64430  0.04284 -0.02007  0.08237\n",
       "OnPix    0.61903  0.55501  0.76564  0.64430  0.99990  0.13915 -0.02882 -0.01198\n",
       "Xbar    -0.03259  0.04569  0.06195  0.04284  0.13915  0.99990 -0.35654 -0.05330\n",
       "Ybar     0.04554 -0.04092  0.02483 -0.02007 -0.02882 -0.35654  0.99990 -0.11861\n",
       "X2bar    0.01430 -0.02502 -0.09860  0.08237 -0.01198 -0.05330 -0.11861  0.99990\n",
       "Y2bar    0.05208  0.09647  0.05707  0.05903 -0.06555 -0.12284 -0.04965 -0.18841\n",
       "XYbar    0.14804  0.15994  0.11501  0.01246 -0.06977  0.08595  0.17830 -0.31775\n",
       "X2Ybar   0.03546 -0.05464  0.01169 -0.01199 -0.07293 -0.34192  0.60034  0.04254\n",
       "XY2bar  -0.04633 -0.00757 -0.04500  0.02638 -0.03885 -0.03211 -0.27162  0.08201\n",
       "Xedge    0.48911  0.27440  0.55720  0.26522  0.62744  0.14431 -0.03672  0.14212\n",
       "XedgeXY  0.09817 -0.00134  0.04565  0.02536  0.01765 -0.25331  0.55500 -0.08481\n",
       "Yedge    0.27348  0.23086  0.26026  0.29752  0.49260  0.12704 -0.07800  0.00655\n",
       "YedgeYX -0.10514 -0.04274 -0.11826 -0.01885 -0.06296  0.24879 -0.20788  0.18288\n",
       "        Y2bar    XYbar    X2Ybar   XY2bar   Xedge    XedgeXY  Yedge    YedgeYX \n",
       "Xbox     0.05208  0.14804  0.03546 -0.04633  0.48911  0.09817  0.27348 -0.10514\n",
       "Ybox     0.09647  0.15994 -0.05464 -0.00757  0.27440 -0.00134  0.23086 -0.04274\n",
       "Width    0.05707  0.11501  0.01169 -0.04500  0.55720  0.04565  0.26026 -0.11826\n",
       "Height   0.05903  0.01246 -0.01199  0.02638  0.26522  0.02536  0.29752 -0.01885\n",
       "OnPix   -0.06555 -0.06977 -0.07293 -0.03885  0.62744  0.01765  0.49260 -0.06296\n",
       "Xbar    -0.12284  0.08595 -0.34192 -0.03211  0.14431 -0.25331  0.12704  0.24879\n",
       "Ybar    -0.04965  0.17830  0.60034 -0.27162 -0.03672  0.55500 -0.07800 -0.20788\n",
       "X2bar   -0.18841 -0.31775  0.04254  0.08201  0.14212 -0.08481  0.00655  0.18288\n",
       "Y2bar    0.99990  0.13199 -0.06011  0.11904 -0.38398 -0.05254  0.27751 -0.06133\n",
       "XYbar    0.13199  0.99990  0.05798 -0.10675 -0.17566  0.02942 -0.08701 -0.11421\n",
       "X2Ybar  -0.06011  0.05798  0.99990  0.06321  0.05356  0.52719 -0.22623 -0.23649\n",
       "XY2bar   0.11904 -0.10675  0.06321  0.99990 -0.00875 -0.18491  0.04969  0.24578\n",
       "Xedge   -0.38398 -0.17566  0.05356 -0.00875  0.99990  0.00285  0.10840 -0.04978\n",
       "XedgeXY -0.05254  0.02942  0.52719 -0.18491  0.00285  0.99990 -0.06440 -0.18757\n",
       "Yedge    0.27751 -0.08701 -0.22623  0.04969  0.10840 -0.06440  0.99990  0.14357\n",
       "YedgeYX -0.06133 -0.11421 -0.23649  0.24578 -0.04978 -0.18757  0.14357  0.99990"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(cm, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue of covariance to produce projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r <- eigen(cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4.29495557278063</li>\n",
       "\t<li>2.62517913014241</li>\n",
       "\t<li>1.7209044356662</li>\n",
       "\t<li>1.36896210456346</li>\n",
       "\t<li>1.05125884002181</li>\n",
       "\t<li>0.979967625455599</li>\n",
       "\t<li>0.889183343142624</li>\n",
       "\t<li>0.625801679971646</li>\n",
       "\t<li>0.595406712435488</li>\n",
       "\t<li>0.491836893068431</li>\n",
       "\t<li>0.426438984186333</li>\n",
       "\t<li>0.266175336243766</li>\n",
       "\t<li>0.253915928929174</li>\n",
       "\t<li>0.21451567419899</li>\n",
       "\t<li>0.119027783502187</li>\n",
       "\t<li>0.0748700356872442</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4.29495557278063\n",
       "\\item 2.62517913014241\n",
       "\\item 1.7209044356662\n",
       "\\item 1.36896210456346\n",
       "\\item 1.05125884002181\n",
       "\\item 0.979967625455599\n",
       "\\item 0.889183343142624\n",
       "\\item 0.625801679971646\n",
       "\\item 0.595406712435488\n",
       "\\item 0.491836893068431\n",
       "\\item 0.426438984186333\n",
       "\\item 0.266175336243766\n",
       "\\item 0.253915928929174\n",
       "\\item 0.21451567419899\n",
       "\\item 0.119027783502187\n",
       "\\item 0.0748700356872442\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4.29495557278063\n",
       "2. 2.62517913014241\n",
       "3. 1.7209044356662\n",
       "4. 1.36896210456346\n",
       "5. 1.05125884002181\n",
       "6. 0.979967625455599\n",
       "7. 0.889183343142624\n",
       "8. 0.625801679971646\n",
       "9. 0.595406712435488\n",
       "10. 0.491836893068431\n",
       "11. 0.426438984186333\n",
       "12. 0.266175336243766\n",
       "13. 0.253915928929174\n",
       "14. 0.21451567419899\n",
       "15. 0.119027783502187\n",
       "16. 0.0748700356872442\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 4.29495557 2.62517913 1.72090444 1.36896210 1.05125884 0.97996763\n",
       " [7] 0.88918334 0.62580168 0.59540671 0.49183689 0.42643898 0.26617534\n",
       "[13] 0.25391593 0.21451567 0.11902778 0.07487004"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r$values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>-0.4272050265</td><td>-0.0840028152</td><td>-0.03776493  </td><td>-0.02207885  </td><td> 0.140038660 </td><td>-0.04076958  </td><td> 0.07340404  </td><td> 0.05887078  </td><td>-0.12659335  </td><td>-0.266568374 </td><td> 0.170693268 </td><td>-0.51413296  </td><td> 0.0217323519</td><td>-0.230772979 </td><td>-0.118369886 </td><td> 0.5745480477</td></tr>\n",
       "\t<tr><td>-0.3995204745</td><td>-0.0098194780</td><td>-0.14604714  </td><td>-0.05986916  </td><td> 0.238531158 </td><td>-0.02520207  </td><td> 0.27500991  </td><td>-0.22366371  </td><td> 0.08466771  </td><td> 0.140933136 </td><td>-0.031336397 </td><td>-0.23294843  </td><td>-0.0548739547</td><td> 0.462973832 </td><td> 0.541604946 </td><td>-0.1980282181</td></tr>\n",
       "\t<tr><td>-0.4376854301</td><td>-0.0557564739</td><td>-0.03215553  </td><td> 0.06230310  </td><td> 0.070946183 </td><td>-0.02910983  </td><td>-0.12490511  </td><td> 0.01861379  </td><td>-0.09573429  </td><td>-0.296475554 </td><td>-0.056206815 </td><td> 0.06643448  </td><td> 0.0939701087</td><td>-0.523363946 </td><td> 0.059537540 </td><td>-0.6226219141</td></tr>\n",
       "\t<tr><td>-0.3995260257</td><td>-0.0001011894</td><td>-0.05129260  </td><td>-0.15550723  </td><td> 0.123599904 </td><td>-0.00852268  </td><td> 0.27879350  </td><td>-0.24782553  </td><td> 0.20215980  </td><td> 0.316109121 </td><td>-0.156817794 </td><td> 0.26399387  </td><td>-0.0003098750</td><td> 0.020096594 </td><td>-0.650838005 </td><td> 0.0006399979</td></tr>\n",
       "\t<tr><td>-0.4166293504</td><td> 0.0351320417</td><td> 0.10028514  </td><td> 0.03658624  </td><td>-0.232528836 </td><td> 0.02491591  </td><td>-0.19846167  </td><td> 0.04756661  </td><td>-0.02931949  </td><td> 0.152203929 </td><td>-0.055028484 </td><td> 0.58093091  </td><td>-0.0110939448</td><td>-0.103339141 </td><td> 0.402438480 </td><td> 0.4244486752</td></tr>\n",
       "\t<tr><td>-0.0536929391</td><td> 0.3296011771</td><td>-0.01153427  </td><td> 0.41581966  </td><td>-0.050861391 </td><td> 0.41412676  </td><td>-0.01855311  </td><td> 0.07624517  </td><td> 0.65692582  </td><td>-0.087775531 </td><td>-0.186168338 </td><td>-0.15677541  </td><td> 0.1720747309</td><td>-0.061823851 </td><td> 0.023146966 </td><td> 0.0522949027</td></tr>\n",
       "\t<tr><td> 0.0129047398</td><td>-0.5088709224</td><td> 0.01949007  </td><td>-0.01862255  </td><td>-0.166577100 </td><td> 0.26460462  </td><td> 0.09259295  </td><td> 0.09567438  </td><td>-0.20317630  </td><td> 0.138616651 </td><td>-0.416977144 </td><td>-0.11263375  </td><td> 0.6107621545</td><td> 0.059519278 </td><td> 0.023771262 </td><td> 0.0218426405</td></tr>\n",
       "\t<tr><td>-0.0004164997</td><td> 0.1117711421</td><td> 0.45247107  </td><td>-0.31349895  </td><td> 0.059153481 </td><td>-0.10855924  </td><td> 0.52248466  </td><td> 0.53899225  </td><td> 0.18101549  </td><td>-0.081313278 </td><td> 0.125046249 </td><td> 0.10613068  </td><td> 0.1552631771</td><td>-0.049598804 </td><td> 0.098706328 </td><td>-0.0558560207</td></tr>\n",
       "\t<tr><td>-0.0083018581</td><td> 0.0185668586</td><td>-0.55072913  </td><td>-0.39401680  </td><td>-0.153760534 </td><td>-0.12385992  </td><td>-0.05653023  </td><td> 0.15325488  </td><td> 0.19097197  </td><td>-0.542333071 </td><td>-0.195737711 </td><td> 0.18424619  </td><td> 0.0798631193</td><td> 0.245061356 </td><td>-0.042109690 </td><td> 0.0656235670</td></tr>\n",
       "\t<tr><td>-0.0281275034</td><td>-0.1419425301</td><td>-0.44347409  </td><td> 0.31693438  </td><td> 0.358027371 </td><td> 0.28671900  </td><td> 0.09793647  </td><td> 0.51856975  </td><td>-0.16681117  </td><td> 0.135145354 </td><td> 0.275454156 </td><td> 0.22797298  </td><td>-0.0774720795</td><td> 0.086565224 </td><td>-0.072141790 </td><td>-0.0202526235</td></tr>\n",
       "\t<tr><td> 0.0238771750</td><td>-0.4721090010</td><td> 0.16861986  </td><td>-0.20760469  </td><td> 0.172281417 </td><td> 0.20461981  </td><td>-0.15710178  </td><td> 0.17607963  </td><td> 0.26324593  </td><td>-0.004478586 </td><td>-0.349696646 </td><td>-0.07225075  </td><td>-0.6081434254</td><td>-0.091312539 </td><td> 0.049458149 </td><td> 0.0180704794</td></tr>\n",
       "\t<tr><td> 0.0162322312</td><td> 0.1833005421</td><td> 0.03158564  </td><td>-0.49633951  </td><td> 0.455079538 </td><td> 0.20135370  </td><td>-0.52705359  </td><td> 0.02035962  </td><td> 0.08778212  </td><td> 0.215371259 </td><td> 0.159251711 </td><td>-0.04381284  </td><td> 0.3316289921</td><td>-0.023772979 </td><td> 0.031219488 </td><td> 0.0075769398</td></tr>\n",
       "\t<tr><td>-0.2892890773</td><td> 0.0131873584</td><td> 0.43122069  </td><td> 0.20488513  </td><td>-0.009897636 </td><td>-0.01611790  </td><td>-0.35131361  </td><td> 0.19628090  </td><td>-0.13621261  </td><td>-0.250458085 </td><td>-0.007810576 </td><td> 0.00107726  </td><td>-0.0007042368</td><td> 0.596940840 </td><td>-0.275567068 </td><td>-0.1108249056</td></tr>\n",
       "\t<tr><td>-0.0131043153</td><td>-0.4565777317</td><td> 0.08463474  </td><td>-0.07105430  </td><td>-0.206524359 </td><td> 0.28665301  </td><td> 0.03069067  </td><td>-0.29023583  </td><td> 0.29133423  </td><td>-0.193058906 </td><td> 0.645533466 </td><td> 0.13047900  </td><td> 0.0765116282</td><td> 0.066153645 </td><td>-0.004827104 </td><td>-0.0548912860</td></tr>\n",
       "\t<tr><td>-0.2077721934</td><td> 0.1651683982</td><td>-0.15600561  </td><td>-0.25730878  </td><td>-0.618550700 </td><td> 0.19640438  </td><td>-0.08613338  </td><td> 0.28840562  </td><td>-0.06309719  </td><td> 0.349808600 </td><td> 0.154960614 </td><td>-0.31407875  </td><td>-0.1903257105</td><td> 0.009130817 </td><td>-0.079708156 </td><td>-0.1885787404</td></tr>\n",
       "\t<tr><td> 0.0365672255</td><td> 0.3090769665</td><td> 0.10688699  </td><td>-0.19133062  </td><td> 0.036314491 </td><td> 0.66475118  </td><td> 0.23942340  </td><td>-0.21735142  </td><td>-0.41424912  </td><td>-0.288787298 </td><td>-0.110964750 </td><td> 0.11205902  </td><td>-0.1629158309</td><td> 0.018216312 </td><td> 0.002229603 </td><td> 0.0239739376</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllll}\n",
       "\t -0.4272050265 & -0.0840028152 & -0.03776493   & -0.02207885   &  0.140038660  & -0.04076958   &  0.07340404   &  0.05887078   & -0.12659335   & -0.266568374  &  0.170693268  & -0.51413296   &  0.0217323519 & -0.230772979  & -0.118369886  &  0.5745480477\\\\\n",
       "\t -0.3995204745 & -0.0098194780 & -0.14604714   & -0.05986916   &  0.238531158  & -0.02520207   &  0.27500991   & -0.22366371   &  0.08466771   &  0.140933136  & -0.031336397  & -0.23294843   & -0.0548739547 &  0.462973832  &  0.541604946  & -0.1980282181\\\\\n",
       "\t -0.4376854301 & -0.0557564739 & -0.03215553   &  0.06230310   &  0.070946183  & -0.02910983   & -0.12490511   &  0.01861379   & -0.09573429   & -0.296475554  & -0.056206815  &  0.06643448   &  0.0939701087 & -0.523363946  &  0.059537540  & -0.6226219141\\\\\n",
       "\t -0.3995260257 & -0.0001011894 & -0.05129260   & -0.15550723   &  0.123599904  & -0.00852268   &  0.27879350   & -0.24782553   &  0.20215980   &  0.316109121  & -0.156817794  &  0.26399387   & -0.0003098750 &  0.020096594  & -0.650838005  &  0.0006399979\\\\\n",
       "\t -0.4166293504 &  0.0351320417 &  0.10028514   &  0.03658624   & -0.232528836  &  0.02491591   & -0.19846167   &  0.04756661   & -0.02931949   &  0.152203929  & -0.055028484  &  0.58093091   & -0.0110939448 & -0.103339141  &  0.402438480  &  0.4244486752\\\\\n",
       "\t -0.0536929391 &  0.3296011771 & -0.01153427   &  0.41581966   & -0.050861391  &  0.41412676   & -0.01855311   &  0.07624517   &  0.65692582   & -0.087775531  & -0.186168338  & -0.15677541   &  0.1720747309 & -0.061823851  &  0.023146966  &  0.0522949027\\\\\n",
       "\t  0.0129047398 & -0.5088709224 &  0.01949007   & -0.01862255   & -0.166577100  &  0.26460462   &  0.09259295   &  0.09567438   & -0.20317630   &  0.138616651  & -0.416977144  & -0.11263375   &  0.6107621545 &  0.059519278  &  0.023771262  &  0.0218426405\\\\\n",
       "\t -0.0004164997 &  0.1117711421 &  0.45247107   & -0.31349895   &  0.059153481  & -0.10855924   &  0.52248466   &  0.53899225   &  0.18101549   & -0.081313278  &  0.125046249  &  0.10613068   &  0.1552631771 & -0.049598804  &  0.098706328  & -0.0558560207\\\\\n",
       "\t -0.0083018581 &  0.0185668586 & -0.55072913   & -0.39401680   & -0.153760534  & -0.12385992   & -0.05653023   &  0.15325488   &  0.19097197   & -0.542333071  & -0.195737711  &  0.18424619   &  0.0798631193 &  0.245061356  & -0.042109690  &  0.0656235670\\\\\n",
       "\t -0.0281275034 & -0.1419425301 & -0.44347409   &  0.31693438   &  0.358027371  &  0.28671900   &  0.09793647   &  0.51856975   & -0.16681117   &  0.135145354  &  0.275454156  &  0.22797298   & -0.0774720795 &  0.086565224  & -0.072141790  & -0.0202526235\\\\\n",
       "\t  0.0238771750 & -0.4721090010 &  0.16861986   & -0.20760469   &  0.172281417  &  0.20461981   & -0.15710178   &  0.17607963   &  0.26324593   & -0.004478586  & -0.349696646  & -0.07225075   & -0.6081434254 & -0.091312539  &  0.049458149  &  0.0180704794\\\\\n",
       "\t  0.0162322312 &  0.1833005421 &  0.03158564   & -0.49633951   &  0.455079538  &  0.20135370   & -0.52705359   &  0.02035962   &  0.08778212   &  0.215371259  &  0.159251711  & -0.04381284   &  0.3316289921 & -0.023772979  &  0.031219488  &  0.0075769398\\\\\n",
       "\t -0.2892890773 &  0.0131873584 &  0.43122069   &  0.20488513   & -0.009897636  & -0.01611790   & -0.35131361   &  0.19628090   & -0.13621261   & -0.250458085  & -0.007810576  &  0.00107726   & -0.0007042368 &  0.596940840  & -0.275567068  & -0.1108249056\\\\\n",
       "\t -0.0131043153 & -0.4565777317 &  0.08463474   & -0.07105430   & -0.206524359  &  0.28665301   &  0.03069067   & -0.29023583   &  0.29133423   & -0.193058906  &  0.645533466  &  0.13047900   &  0.0765116282 &  0.066153645  & -0.004827104  & -0.0548912860\\\\\n",
       "\t -0.2077721934 &  0.1651683982 & -0.15600561   & -0.25730878   & -0.618550700  &  0.19640438   & -0.08613338   &  0.28840562   & -0.06309719   &  0.349808600  &  0.154960614  & -0.31407875   & -0.1903257105 &  0.009130817  & -0.079708156  & -0.1885787404\\\\\n",
       "\t  0.0365672255 &  0.3090769665 &  0.10688699   & -0.19133062   &  0.036314491  &  0.66475118   &  0.23942340   & -0.21735142   & -0.41424912   & -0.288787298  & -0.110964750  &  0.11205902   & -0.1629158309 &  0.018216312  &  0.002229603  &  0.0239739376\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| -0.4272050265 | -0.0840028152 | -0.03776493   | -0.02207885   |  0.140038660  | -0.04076958   |  0.07340404   |  0.05887078   | -0.12659335   | -0.266568374  |  0.170693268  | -0.51413296   |  0.0217323519 | -0.230772979  | -0.118369886  |  0.5745480477 | \n",
       "| -0.3995204745 | -0.0098194780 | -0.14604714   | -0.05986916   |  0.238531158  | -0.02520207   |  0.27500991   | -0.22366371   |  0.08466771   |  0.140933136  | -0.031336397  | -0.23294843   | -0.0548739547 |  0.462973832  |  0.541604946  | -0.1980282181 | \n",
       "| -0.4376854301 | -0.0557564739 | -0.03215553   |  0.06230310   |  0.070946183  | -0.02910983   | -0.12490511   |  0.01861379   | -0.09573429   | -0.296475554  | -0.056206815  |  0.06643448   |  0.0939701087 | -0.523363946  |  0.059537540  | -0.6226219141 | \n",
       "| -0.3995260257 | -0.0001011894 | -0.05129260   | -0.15550723   |  0.123599904  | -0.00852268   |  0.27879350   | -0.24782553   |  0.20215980   |  0.316109121  | -0.156817794  |  0.26399387   | -0.0003098750 |  0.020096594  | -0.650838005  |  0.0006399979 | \n",
       "| -0.4166293504 |  0.0351320417 |  0.10028514   |  0.03658624   | -0.232528836  |  0.02491591   | -0.19846167   |  0.04756661   | -0.02931949   |  0.152203929  | -0.055028484  |  0.58093091   | -0.0110939448 | -0.103339141  |  0.402438480  |  0.4244486752 | \n",
       "| -0.0536929391 |  0.3296011771 | -0.01153427   |  0.41581966   | -0.050861391  |  0.41412676   | -0.01855311   |  0.07624517   |  0.65692582   | -0.087775531  | -0.186168338  | -0.15677541   |  0.1720747309 | -0.061823851  |  0.023146966  |  0.0522949027 | \n",
       "|  0.0129047398 | -0.5088709224 |  0.01949007   | -0.01862255   | -0.166577100  |  0.26460462   |  0.09259295   |  0.09567438   | -0.20317630   |  0.138616651  | -0.416977144  | -0.11263375   |  0.6107621545 |  0.059519278  |  0.023771262  |  0.0218426405 | \n",
       "| -0.0004164997 |  0.1117711421 |  0.45247107   | -0.31349895   |  0.059153481  | -0.10855924   |  0.52248466   |  0.53899225   |  0.18101549   | -0.081313278  |  0.125046249  |  0.10613068   |  0.1552631771 | -0.049598804  |  0.098706328  | -0.0558560207 | \n",
       "| -0.0083018581 |  0.0185668586 | -0.55072913   | -0.39401680   | -0.153760534  | -0.12385992   | -0.05653023   |  0.15325488   |  0.19097197   | -0.542333071  | -0.195737711  |  0.18424619   |  0.0798631193 |  0.245061356  | -0.042109690  |  0.0656235670 | \n",
       "| -0.0281275034 | -0.1419425301 | -0.44347409   |  0.31693438   |  0.358027371  |  0.28671900   |  0.09793647   |  0.51856975   | -0.16681117   |  0.135145354  |  0.275454156  |  0.22797298   | -0.0774720795 |  0.086565224  | -0.072141790  | -0.0202526235 | \n",
       "|  0.0238771750 | -0.4721090010 |  0.16861986   | -0.20760469   |  0.172281417  |  0.20461981   | -0.15710178   |  0.17607963   |  0.26324593   | -0.004478586  | -0.349696646  | -0.07225075   | -0.6081434254 | -0.091312539  |  0.049458149  |  0.0180704794 | \n",
       "|  0.0162322312 |  0.1833005421 |  0.03158564   | -0.49633951   |  0.455079538  |  0.20135370   | -0.52705359   |  0.02035962   |  0.08778212   |  0.215371259  |  0.159251711  | -0.04381284   |  0.3316289921 | -0.023772979  |  0.031219488  |  0.0075769398 | \n",
       "| -0.2892890773 |  0.0131873584 |  0.43122069   |  0.20488513   | -0.009897636  | -0.01611790   | -0.35131361   |  0.19628090   | -0.13621261   | -0.250458085  | -0.007810576  |  0.00107726   | -0.0007042368 |  0.596940840  | -0.275567068  | -0.1108249056 | \n",
       "| -0.0131043153 | -0.4565777317 |  0.08463474   | -0.07105430   | -0.206524359  |  0.28665301   |  0.03069067   | -0.29023583   |  0.29133423   | -0.193058906  |  0.645533466  |  0.13047900   |  0.0765116282 |  0.066153645  | -0.004827104  | -0.0548912860 | \n",
       "| -0.2077721934 |  0.1651683982 | -0.15600561   | -0.25730878   | -0.618550700  |  0.19640438   | -0.08613338   |  0.28840562   | -0.06309719   |  0.349808600  |  0.154960614  | -0.31407875   | -0.1903257105 |  0.009130817  | -0.079708156  | -0.1885787404 | \n",
       "|  0.0365672255 |  0.3090769665 |  0.10688699   | -0.19133062   |  0.036314491  |  0.66475118   |  0.23942340   | -0.21735142   | -0.41424912   | -0.288787298  | -0.110964750  |  0.11205902   | -0.1629158309 |  0.018216312  |  0.002229603  |  0.0239739376 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]          [,2]          [,3]        [,4]        [,5]        \n",
       " [1,] -0.4272050265 -0.0840028152 -0.03776493 -0.02207885  0.140038660\n",
       " [2,] -0.3995204745 -0.0098194780 -0.14604714 -0.05986916  0.238531158\n",
       " [3,] -0.4376854301 -0.0557564739 -0.03215553  0.06230310  0.070946183\n",
       " [4,] -0.3995260257 -0.0001011894 -0.05129260 -0.15550723  0.123599904\n",
       " [5,] -0.4166293504  0.0351320417  0.10028514  0.03658624 -0.232528836\n",
       " [6,] -0.0536929391  0.3296011771 -0.01153427  0.41581966 -0.050861391\n",
       " [7,]  0.0129047398 -0.5088709224  0.01949007 -0.01862255 -0.166577100\n",
       " [8,] -0.0004164997  0.1117711421  0.45247107 -0.31349895  0.059153481\n",
       " [9,] -0.0083018581  0.0185668586 -0.55072913 -0.39401680 -0.153760534\n",
       "[10,] -0.0281275034 -0.1419425301 -0.44347409  0.31693438  0.358027371\n",
       "[11,]  0.0238771750 -0.4721090010  0.16861986 -0.20760469  0.172281417\n",
       "[12,]  0.0162322312  0.1833005421  0.03158564 -0.49633951  0.455079538\n",
       "[13,] -0.2892890773  0.0131873584  0.43122069  0.20488513 -0.009897636\n",
       "[14,] -0.0131043153 -0.4565777317  0.08463474 -0.07105430 -0.206524359\n",
       "[15,] -0.2077721934  0.1651683982 -0.15600561 -0.25730878 -0.618550700\n",
       "[16,]  0.0365672255  0.3090769665  0.10688699 -0.19133062  0.036314491\n",
       "      [,6]        [,7]        [,8]        [,9]        [,10]        [,11]       \n",
       " [1,] -0.04076958  0.07340404  0.05887078 -0.12659335 -0.266568374  0.170693268\n",
       " [2,] -0.02520207  0.27500991 -0.22366371  0.08466771  0.140933136 -0.031336397\n",
       " [3,] -0.02910983 -0.12490511  0.01861379 -0.09573429 -0.296475554 -0.056206815\n",
       " [4,] -0.00852268  0.27879350 -0.24782553  0.20215980  0.316109121 -0.156817794\n",
       " [5,]  0.02491591 -0.19846167  0.04756661 -0.02931949  0.152203929 -0.055028484\n",
       " [6,]  0.41412676 -0.01855311  0.07624517  0.65692582 -0.087775531 -0.186168338\n",
       " [7,]  0.26460462  0.09259295  0.09567438 -0.20317630  0.138616651 -0.416977144\n",
       " [8,] -0.10855924  0.52248466  0.53899225  0.18101549 -0.081313278  0.125046249\n",
       " [9,] -0.12385992 -0.05653023  0.15325488  0.19097197 -0.542333071 -0.195737711\n",
       "[10,]  0.28671900  0.09793647  0.51856975 -0.16681117  0.135145354  0.275454156\n",
       "[11,]  0.20461981 -0.15710178  0.17607963  0.26324593 -0.004478586 -0.349696646\n",
       "[12,]  0.20135370 -0.52705359  0.02035962  0.08778212  0.215371259  0.159251711\n",
       "[13,] -0.01611790 -0.35131361  0.19628090 -0.13621261 -0.250458085 -0.007810576\n",
       "[14,]  0.28665301  0.03069067 -0.29023583  0.29133423 -0.193058906  0.645533466\n",
       "[15,]  0.19640438 -0.08613338  0.28840562 -0.06309719  0.349808600  0.154960614\n",
       "[16,]  0.66475118  0.23942340 -0.21735142 -0.41424912 -0.288787298 -0.110964750\n",
       "      [,12]       [,13]         [,14]        [,15]        [,16]        \n",
       " [1,] -0.51413296  0.0217323519 -0.230772979 -0.118369886  0.5745480477\n",
       " [2,] -0.23294843 -0.0548739547  0.462973832  0.541604946 -0.1980282181\n",
       " [3,]  0.06643448  0.0939701087 -0.523363946  0.059537540 -0.6226219141\n",
       " [4,]  0.26399387 -0.0003098750  0.020096594 -0.650838005  0.0006399979\n",
       " [5,]  0.58093091 -0.0110939448 -0.103339141  0.402438480  0.4244486752\n",
       " [6,] -0.15677541  0.1720747309 -0.061823851  0.023146966  0.0522949027\n",
       " [7,] -0.11263375  0.6107621545  0.059519278  0.023771262  0.0218426405\n",
       " [8,]  0.10613068  0.1552631771 -0.049598804  0.098706328 -0.0558560207\n",
       " [9,]  0.18424619  0.0798631193  0.245061356 -0.042109690  0.0656235670\n",
       "[10,]  0.22797298 -0.0774720795  0.086565224 -0.072141790 -0.0202526235\n",
       "[11,] -0.07225075 -0.6081434254 -0.091312539  0.049458149  0.0180704794\n",
       "[12,] -0.04381284  0.3316289921 -0.023772979  0.031219488  0.0075769398\n",
       "[13,]  0.00107726 -0.0007042368  0.596940840 -0.275567068 -0.1108249056\n",
       "[14,]  0.13047900  0.0765116282  0.066153645 -0.004827104 -0.0548912860\n",
       "[15,] -0.31407875 -0.1903257105  0.009130817 -0.079708156 -0.1885787404\n",
       "[16,]  0.11205902 -0.1629158309  0.018216312  0.002229603  0.0239739376"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r$vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lettersPca <- mtx %*% r$vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"New\" covariance matrix (now diagonal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>4.295 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>2.6252</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>1.7209</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>1.369 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>1.0513</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.98  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.8892</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.6258</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.5954</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.4918</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.4264</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.2662</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.2539</td><td>0.0000</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.2145</td><td>0.000 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.119 </td><td>0.0000</td></tr>\n",
       "\t<tr><td>0.000 </td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0000</td><td>0.00  </td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.000 </td><td>0.0749</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllll}\n",
       "\t 4.295  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 2.6252 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 1.7209 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 1.369  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 1.0513 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.98   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.8892 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.6258 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.5954 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.4918 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.4264 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.2662 & 0.0000 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.2539 & 0.0000 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.2145 & 0.000  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.119  & 0.0000\\\\\n",
       "\t 0.000  & 0.0000 & 0.0000 & 0.000  & 0.0000 & 0.00   & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.000  & 0.0749\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 4.295  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 2.6252 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 1.7209 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 1.369  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 1.0513 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.98   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.8892 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.6258 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.5954 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.4918 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.4264 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.2662 | 0.0000 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.2539 | 0.0000 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.2145 | 0.000  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.119  | 0.0000 | \n",
       "| 0.000  | 0.0000 | 0.0000 | 0.000  | 0.0000 | 0.00   | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.000  | 0.0749 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]  [,2]   [,3]   [,4]  [,5]   [,6] [,7]   [,8]   [,9]   [,10]  [,11] \n",
       " [1,] 4.295 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [2,] 0.000 2.6252 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [3,] 0.000 0.0000 1.7209 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [4,] 0.000 0.0000 0.0000 1.369 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [5,] 0.000 0.0000 0.0000 0.000 1.0513 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [6,] 0.000 0.0000 0.0000 0.000 0.0000 0.98 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       " [7,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.8892 0.0000 0.0000 0.0000 0.0000\n",
       " [8,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.6258 0.0000 0.0000 0.0000\n",
       " [9,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.5954 0.0000 0.0000\n",
       "[10,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.4918 0.0000\n",
       "[11,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.4264\n",
       "[12,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "[13,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "[14,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "[15,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "[16,] 0.000 0.0000 0.0000 0.000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "      [,12]  [,13]  [,14]  [,15] [,16] \n",
       " [1,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [2,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [3,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [4,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [5,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [6,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [7,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [8,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       " [9,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       "[10,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       "[11,] 0.0000 0.0000 0.0000 0.000 0.0000\n",
       "[12,] 0.2662 0.0000 0.0000 0.000 0.0000\n",
       "[13,] 0.0000 0.2539 0.0000 0.000 0.0000\n",
       "[14,] 0.0000 0.0000 0.2145 0.000 0.0000\n",
       "[15,] 0.0000 0.0000 0.0000 0.119 0.0000\n",
       "[16,] 0.0000 0.0000 0.0000 0.000 0.0749"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(t(lettersPca) %*% lettersPca / (nrow(lettersPca) + 1), 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Amount of variance \"explained\" through first N dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.26846156811336</li>\n",
       "\t<li>0.432551671937233</li>\n",
       "\t<li>0.540118955356903</li>\n",
       "\t<li>0.625687643333095</li>\n",
       "\t<li>0.691397891530744</li>\n",
       "\t<li>0.752651993225633</li>\n",
       "\t<li>0.808231509845825</li>\n",
       "\t<li>0.847348026300126</li>\n",
       "\t<li>0.88456466730537</li>\n",
       "\t<li>0.915307547256436</li>\n",
       "\t<li>0.941962649145001</li>\n",
       "\t<li>0.958600271339272</li>\n",
       "\t<li>0.974471603951254</li>\n",
       "\t<li>0.987880174378694</li>\n",
       "\t<li>0.995320154808426</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.26846156811336\n",
       "\\item 0.432551671937233\n",
       "\\item 0.540118955356903\n",
       "\\item 0.625687643333095\n",
       "\\item 0.691397891530744\n",
       "\\item 0.752651993225633\n",
       "\\item 0.808231509845825\n",
       "\\item 0.847348026300126\n",
       "\\item 0.88456466730537\n",
       "\\item 0.915307547256436\n",
       "\\item 0.941962649145001\n",
       "\\item 0.958600271339272\n",
       "\\item 0.974471603951254\n",
       "\\item 0.987880174378694\n",
       "\\item 0.995320154808426\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.26846156811336\n",
       "2. 0.432551671937233\n",
       "3. 0.540118955356903\n",
       "4. 0.625687643333095\n",
       "5. 0.691397891530744\n",
       "6. 0.752651993225633\n",
       "7. 0.808231509845825\n",
       "8. 0.847348026300126\n",
       "9. 0.88456466730537\n",
       "10. 0.915307547256436\n",
       "11. 0.941962649145001\n",
       "12. 0.958600271339272\n",
       "13. 0.974471603951254\n",
       "14. 0.987880174378694\n",
       "15. 0.995320154808426\n",
       "16. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0.2684616 0.4325517 0.5401190 0.6256876 0.6913979 0.7526520 0.8082315\n",
       " [8] 0.8473480 0.8845647 0.9153075 0.9419626 0.9586003 0.9744716 0.9878802\n",
       "[15] 0.9953202 1.0000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cumsum(r$values) /  sum(r$values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lettersDf <- data.frame(class = letters$Letter, pca = lettersPca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>class</th><th scope=col>pca.1</th><th scope=col>pca.2</th><th scope=col>pca.3</th><th scope=col>pca.4</th><th scope=col>pca.5</th><th scope=col>pca.6</th><th scope=col>pca.7</th><th scope=col>pca.8</th><th scope=col>pca.9</th><th scope=col>pca.10</th><th scope=col>pca.11</th><th scope=col>pca.12</th><th scope=col>pca.13</th><th scope=col>pca.14</th><th scope=col>pca.15</th><th scope=col>pca.16</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>T           </td><td> 2.0802826  </td><td>-1.7214273  </td><td>-0.7101134  </td><td> 0.01488226 </td><td> 0.3879182  </td><td> 0.8110448  </td><td>-0.1051808  </td><td>-1.6358895  </td><td> 0.5568141  </td><td> 0.3497204  </td><td>-2.4972454  </td><td>-0.6447702  </td><td> 0.674839787</td><td> 0.3138484  </td><td> 0.36215736 </td><td> 0.1772178  </td></tr>\n",
       "\t<tr><td>I           </td><td>-0.3693641  </td><td> 2.0140751  </td><td>-1.1456671  </td><td> 0.75540463 </td><td> 1.5010561  </td><td> 1.5950273  </td><td> 1.4777231  </td><td>-0.0472795  </td><td> 0.2937318  </td><td> 0.6616662  </td><td> 1.0947401  </td><td>-0.4971983  </td><td>-0.012944916</td><td> 0.9430876  </td><td>-0.07775341 </td><td> 0.3900517  </td></tr>\n",
       "\t<tr><td>D           </td><td>-1.6543080  </td><td> 1.7549411  </td><td>-1.2970617  </td><td> 1.33254595 </td><td> 0.3035506  </td><td> 0.5337721  </td><td> 0.4464274  </td><td>-0.7852911  </td><td> 0.2501475  </td><td> 0.1187188  </td><td>-0.6188393  </td><td> 0.8433984  </td><td> 0.168779558</td><td> 0.3678095  </td><td> 0.19275677 </td><td> 0.1881952  </td></tr>\n",
       "\t<tr><td>N           </td><td>-1.4902434  </td><td>-0.5088705  </td><td> 0.8328723  </td><td>-1.11160001 </td><td> 0.3503288  </td><td>-0.5932453  </td><td>-0.4235371  </td><td>-1.6469317  </td><td>-0.5368484  </td><td>-1.1233987  </td><td> 0.5598075  </td><td>-1.0044602  </td><td> 1.452820112</td><td> 0.9258707  </td><td>-0.01811037 </td><td> 0.2412374  </td></tr>\n",
       "\t<tr><td>G           </td><td> 3.0809040  </td><td> 2.0697897  </td><td> 0.2900172  </td><td>-0.67184999 </td><td>-0.8423558  </td><td> 0.5619149  </td><td>-0.2954488  </td><td> 0.4259705  </td><td>-0.3061814  </td><td>-0.6522141  </td><td>-0.1353708  </td><td>-0.4842026  </td><td>-0.008748236</td><td>-0.5762434  </td><td> 0.16739361 </td><td> 0.0253058  </td></tr>\n",
       "\t<tr><td>S           </td><td>-0.9047219  </td><td> 0.5109631  </td><td>-1.3424739  </td><td>-1.44516116 </td><td>-1.9654616  </td><td>-0.5804360  </td><td> 1.4327417  </td><td>-0.2092341  </td><td> 1.3448264  </td><td> 0.4512934  </td><td>-0.8537541  </td><td>-0.8469901  </td><td>-0.066747310</td><td> 0.1238721  </td><td> 0.05138294 </td><td>-0.4226609  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllllllll}\n",
       " class & pca.1 & pca.2 & pca.3 & pca.4 & pca.5 & pca.6 & pca.7 & pca.8 & pca.9 & pca.10 & pca.11 & pca.12 & pca.13 & pca.14 & pca.15 & pca.16\\\\\n",
       "\\hline\n",
       "\t T            &  2.0802826   & -1.7214273   & -0.7101134   &  0.01488226  &  0.3879182   &  0.8110448   & -0.1051808   & -1.6358895   &  0.5568141   &  0.3497204   & -2.4972454   & -0.6447702   &  0.674839787 &  0.3138484   &  0.36215736  &  0.1772178  \\\\\n",
       "\t I            & -0.3693641   &  2.0140751   & -1.1456671   &  0.75540463  &  1.5010561   &  1.5950273   &  1.4777231   & -0.0472795   &  0.2937318   &  0.6616662   &  1.0947401   & -0.4971983   & -0.012944916 &  0.9430876   & -0.07775341  &  0.3900517  \\\\\n",
       "\t D            & -1.6543080   &  1.7549411   & -1.2970617   &  1.33254595  &  0.3035506   &  0.5337721   &  0.4464274   & -0.7852911   &  0.2501475   &  0.1187188   & -0.6188393   &  0.8433984   &  0.168779558 &  0.3678095   &  0.19275677  &  0.1881952  \\\\\n",
       "\t N            & -1.4902434   & -0.5088705   &  0.8328723   & -1.11160001  &  0.3503288   & -0.5932453   & -0.4235371   & -1.6469317   & -0.5368484   & -1.1233987   &  0.5598075   & -1.0044602   &  1.452820112 &  0.9258707   & -0.01811037  &  0.2412374  \\\\\n",
       "\t G            &  3.0809040   &  2.0697897   &  0.2900172   & -0.67184999  & -0.8423558   &  0.5619149   & -0.2954488   &  0.4259705   & -0.3061814   & -0.6522141   & -0.1353708   & -0.4842026   & -0.008748236 & -0.5762434   &  0.16739361  &  0.0253058  \\\\\n",
       "\t S            & -0.9047219   &  0.5109631   & -1.3424739   & -1.44516116  & -1.9654616   & -0.5804360   &  1.4327417   & -0.2092341   &  1.3448264   &  0.4512934   & -0.8537541   & -0.8469901   & -0.066747310 &  0.1238721   &  0.05138294  & -0.4226609  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "class | pca.1 | pca.2 | pca.3 | pca.4 | pca.5 | pca.6 | pca.7 | pca.8 | pca.9 | pca.10 | pca.11 | pca.12 | pca.13 | pca.14 | pca.15 | pca.16 | \n",
       "|---|---|---|---|---|---|\n",
       "| T            |  2.0802826   | -1.7214273   | -0.7101134   |  0.01488226  |  0.3879182   |  0.8110448   | -0.1051808   | -1.6358895   |  0.5568141   |  0.3497204   | -2.4972454   | -0.6447702   |  0.674839787 |  0.3138484   |  0.36215736  |  0.1772178   | \n",
       "| I            | -0.3693641   |  2.0140751   | -1.1456671   |  0.75540463  |  1.5010561   |  1.5950273   |  1.4777231   | -0.0472795   |  0.2937318   |  0.6616662   |  1.0947401   | -0.4971983   | -0.012944916 |  0.9430876   | -0.07775341  |  0.3900517   | \n",
       "| D            | -1.6543080   |  1.7549411   | -1.2970617   |  1.33254595  |  0.3035506   |  0.5337721   |  0.4464274   | -0.7852911   |  0.2501475   |  0.1187188   | -0.6188393   |  0.8433984   |  0.168779558 |  0.3678095   |  0.19275677  |  0.1881952   | \n",
       "| N            | -1.4902434   | -0.5088705   |  0.8328723   | -1.11160001  |  0.3503288   | -0.5932453   | -0.4235371   | -1.6469317   | -0.5368484   | -1.1233987   |  0.5598075   | -1.0044602   |  1.452820112 |  0.9258707   | -0.01811037  |  0.2412374   | \n",
       "| G            |  3.0809040   |  2.0697897   |  0.2900172   | -0.67184999  | -0.8423558   |  0.5619149   | -0.2954488   |  0.4259705   | -0.3061814   | -0.6522141   | -0.1353708   | -0.4842026   | -0.008748236 | -0.5762434   |  0.16739361  |  0.0253058   | \n",
       "| S            | -0.9047219   |  0.5109631   | -1.3424739   | -1.44516116  | -1.9654616   | -0.5804360   |  1.4327417   | -0.2092341   |  1.3448264   |  0.4512934   | -0.8537541   | -0.8469901   | -0.066747310 |  0.1238721   |  0.05138294  | -0.4226609   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  class pca.1      pca.2      pca.3      pca.4       pca.5      pca.6     \n",
       "1 T      2.0802826 -1.7214273 -0.7101134  0.01488226  0.3879182  0.8110448\n",
       "2 I     -0.3693641  2.0140751 -1.1456671  0.75540463  1.5010561  1.5950273\n",
       "3 D     -1.6543080  1.7549411 -1.2970617  1.33254595  0.3035506  0.5337721\n",
       "4 N     -1.4902434 -0.5088705  0.8328723 -1.11160001  0.3503288 -0.5932453\n",
       "5 G      3.0809040  2.0697897  0.2900172 -0.67184999 -0.8423558  0.5619149\n",
       "6 S     -0.9047219  0.5109631 -1.3424739 -1.44516116 -1.9654616 -0.5804360\n",
       "  pca.7      pca.8      pca.9      pca.10     pca.11     pca.12    \n",
       "1 -0.1051808 -1.6358895  0.5568141  0.3497204 -2.4972454 -0.6447702\n",
       "2  1.4777231 -0.0472795  0.2937318  0.6616662  1.0947401 -0.4971983\n",
       "3  0.4464274 -0.7852911  0.2501475  0.1187188 -0.6188393  0.8433984\n",
       "4 -0.4235371 -1.6469317 -0.5368484 -1.1233987  0.5598075 -1.0044602\n",
       "5 -0.2954488  0.4259705 -0.3061814 -0.6522141 -0.1353708 -0.4842026\n",
       "6  1.4327417 -0.2092341  1.3448264  0.4512934 -0.8537541 -0.8469901\n",
       "  pca.13       pca.14     pca.15      pca.16    \n",
       "1  0.674839787  0.3138484  0.36215736  0.1772178\n",
       "2 -0.012944916  0.9430876 -0.07775341  0.3900517\n",
       "3  0.168779558  0.3678095  0.19275677  0.1881952\n",
       "4  1.452820112  0.9258707 -0.01811037  0.2412374\n",
       "5 -0.008748236 -0.5762434  0.16739361  0.0253058\n",
       "6 -0.066747310  0.1238721  0.05138294 -0.4226609"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(lettersDf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "decim <- sample_frac(lettersDf, 0.025)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First two principal axes, showing some order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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hQEOwAIvtwse85oe2sbX98oNDarGpuF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\nwDEM08fd/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HadK0wa4zuNjSQ+Tz9Hnz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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "ggplot(decim, aes(label = class, pca.1, pca.2, colour = class)) + geom_text()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}